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Quiz

Lesson 1: Integration Techniques (Substitution and By Parts) and Definite Integrals — Picture questions (exam style)

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  • Questions count: 86
  • Passing grade: 60%
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1.
If f″(x) = 6⋅x + 12, f′(0) = 2 and f(0) = -2, which option is correct?
If f″(x) = 6⋅x + 12, f′(0) = 2 and f(0) = -2, which option is correct?
f(2) = 34, f′(2) = 38
f(2) = 36, f′(2) = 39
f(2) = 36, f′(2) = 24
f(2) = 34, f′(2) = 2
2.
A curve y = F(x) passes through (1, 3) and its gradient is the expression shown. Find y when x = 2.
A curve y = F(x) passes through (1, 3) and its gradient is the expression shown. Find y when x = 2.
11.8
18.6
15.2
44
3.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
2.197
0.6667
1.099
-1.099
4.
If f″(x) = 12⋅x + 2, f′(0) = 1 and f(0) = 3, which option is correct?
If f″(x) = 12⋅x + 2, f′(0) = 1 and f(0) = 3, which option is correct?
f(2) = 22, f′(2) = 1
f(2) = 28, f′(2) = 26
f(2) = 26, f′(2) = 29
f(2) = 25, f′(2) = 29
5.
A curve y = F(x) passes through (1, 6) and its gradient is the expression shown. Find y when x = 3.
A curve y = F(x) passes through (1, 6) and its gradient is the expression shown. Find y when x = 3.
16.5
6.325
14.05
11.61
6.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
-1
1
2
1.571
7.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
-0.3071
0.6142
0.75
0.3071
8.
If f″(x) = 8 - 6⋅x, f′(0) = 2 and f(0) = 0, which option is correct?
If f″(x) = 8 - 6⋅x, f′(0) = 2 and f(0) = 0, which option is correct?
f(1) = 5, f′(1) = 8
f(1) = 7, f′(1) = 7
f(1) = 5, f′(1) = 7
f(1) = 7, f′(1) = 2
9.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
-1.386
1.386
0.5
2.773
10.
If f″(x) = 8 - 6⋅x, f′(0) = -2 and f(0) = -1, which option is correct?
If f″(x) = 8 - 6⋅x, f′(0) = -2 and f(0) = -1, which option is correct?
f(2) = 4, f′(2) = 3
f(2) = 3, f′(2) = -2
f(2) = 3, f′(2) = 2
f(2) = 1, f′(2) = -2
11.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
-4.575
4.575
9.149
7.389
12.
A curve y = F(x) passes through (0, 6) and its gradient is the expression shown. Find y when x = 1.
A curve y = F(x) passes through (0, 6) and its gradient is the expression shown. Find y when x = 1.
11.19
5.695
0.1945
9.389
13.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
0.5754
-0.2877
0.5
0.2877
14.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
0
0.6667
-0.3333
0.3333
15.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
0.6
2.303
4.605
-2.303
16.
If f″(x) = 4, f′(0) = 0 and f(0) = 2, which option is correct?
If f″(x) = 4, f′(0) = 0 and f(0) = 2, which option is correct?
f(2) = 10, f′(2) = 0
f(2) = 8, f′(2) = 0
f(2) = 10, f′(2) = 8
f(2) = 10, f′(2) = 9
17.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
-0.75
1.5
2
0.75
18.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
-224.2
224.2
448.5
109.2
19.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
-0.5
0.5
1
0
20.
A curve y = F(x) passes through (0, 2) and its gradient is the expression shown. Find y when x = 1.
A curve y = F(x) passes through (0, 2) and its gradient is the expression shown. Find y when x = 1.
1.482
-2.99
0.7022
1.222
21.
If f″(x) = 4, f′(0) = 1 and f(0) = -1, which option is correct?
If f″(x) = 4, f′(0) = 1 and f(0) = -1, which option is correct?
f(2) = 9, f′(2) = 9
f(2) = 10, f′(2) = 1
f(2) = 8, f′(2) = 4
f(2) = 9, f′(2) = 10
22.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
806.9
-224.2
224.2
448.5
23.
A curve y = F(x) passes through (0, 6) and its gradient is the expression shown. Find y when x = 1.
A curve y = F(x) passes through (0, 6) and its gradient is the expression shown. Find y when x = 1.
-5.406
-4.11
4.594
-0.4057
24.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
-0.1111
0.5236
0.1111
0.2222
25.
A curve y = F(x) passes through (2, -1) and its gradient is the expression shown. Find y when x = 4.
A curve y = F(x) passes through (2, -1) and its gradient is the expression shown. Find y when x = 4.
3.837
-2.387
4.275
4.713
26.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
-1.609
3.219
1.609
0.8
27.
A curve y = F(x) passes through (0, 6) and its gradient is the expression shown. Find y when x = 2.
A curve y = F(x) passes through (0, 6) and its gradient is the expression shown. Find y when x = 2.
6.595
0.5945
-0.4286
-5.405
28.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
-1.296
1.099
1.296
2.592
29.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
1.705
0.5455
3.409
-1.705
30.
A curve y = F(x) passes through (2, -5) and its gradient is the expression shown. Find y when x = 4.
A curve y = F(x) passes through (2, -5) and its gradient is the expression shown. Find y when x = 4.
-0.3971
3.127
-1.484
6.651
31.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
20.09
9.149
-4.575
4.575
32.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
-1.75
1.75
3.5
4
33.
A curve y = F(x) passes through (0, -4) and its gradient is the expression shown. Find y when x = 2.
A curve y = F(x) passes through (0, -4) and its gradient is the expression shown. Find y when x = 2.
3.976
1.479
2.976
4.976
34.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
69.33
-34.67
72
34.67
35.
A curve y = F(x) passes through (0, 5) and its gradient is the expression shown. Find y when x = 1.
A curve y = F(x) passes through (0, 5) and its gradient is the expression shown. Find y when x = 1.
-3
2
4
7
36.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
-41.2
82.4
109.2
41.2
37.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
-1.25
2.5
1.25
3
38.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
41.33
-20.67
20.67
50
39.
A curve y = F(x) passes through (2, 1) and its gradient is the expression shown. Find y when x = 4.
A curve y = F(x) passes through (2, 1) and its gradient is the expression shown. Find y when x = 4.
164.8
144.6
191
167.8
40.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
0.7854
1
1.571
-0.7854
41.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
2.097
-2.097
2.718
4.195
42.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
7.389
2.097
-2.097
4.195
43.
If f″(x) = 10, f′(0) = -3 and f(0) = 1, which option is correct?
If f″(x) = 10, f′(0) = -3 and f(0) = 1, which option is correct?
f(1) = 3, f′(1) = 8
f(1) = 0, f′(1) = -3
f(1) = 2, f′(1) = 8
f(1) = 3, f′(1) = 7
44.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
0.75
0.6319
1.264
-0.6319
45.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
1210
504.5
1009
-504.5
46.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
2.944
-2.944
3.296
5.888
47.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
16.78
14.78
-8.389
8.389
48.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
-0.5236
0
1.047
0.5236
49.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
98
105.3
-52.67
52.67
50.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
1828
-1828
3993
3656
51.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
0.8109
0.4055
0.6667
-0.4055
52.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
-7203
2.431e+04
7203
1.441e+04
53.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
0
0.5
-0.25
0.25
54.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
1.74
-1
2
1
55.
A curve y = F(x) passes through (0, 3) and its gradient is the expression shown. Find y when x = 2.
A curve y = F(x) passes through (0, 3) and its gradient is the expression shown. Find y when x = 2.
1.325
0.4932
5.325
-2.675
56.
A curve y = F(x) passes through (2, 1) and its gradient is the expression shown. Find y when x = 4.
A curve y = F(x) passes through (2, 1) and its gradient is the expression shown. Find y when x = 4.
6.273
11.73
3
9
57.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
1
1.386
0.6931
-0.6931
58.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
1.571
0
-1.571
3.142
59.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
-0.25
0.7854
0.5
0.25
60.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
-1250
3000
2500
1250
61.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
2
2.718
-1
1
62.
A curve y = F(x) passes through (1, -1) and its gradient is the expression shown. Find y when x = 2.
A curve y = F(x) passes through (1, -1) and its gradient is the expression shown. Find y when x = 2.
-0.2621
5.379
9.506
1.252
63.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
2
8.389
-8.389
16.78
64.
A curve y = F(x) passes through (0, -3) and its gradient is the expression shown. Find y when x = 2.
A curve y = F(x) passes through (0, -3) and its gradient is the expression shown. Find y when x = 2.
10.99
23.65
8.66
17.32
65.
A curve y = F(x) passes through (0, 3) and its gradient is the expression shown. Find y when x = 1.
A curve y = F(x) passes through (0, 3) and its gradient is the expression shown. Find y when x = 1.
5.143
1.143
-2.857
1.922
66.
If f″(x) = 10 - 18⋅x, f′(0) = 1 and f(0) = -1, which option is correct?
If f″(x) = 10 - 18⋅x, f′(0) = 1 and f(0) = -1, which option is correct?
f(1) = 3, f′(1) = 2
f(1) = 2, f′(1) = -8
f(1) = 2, f′(1) = 2
f(1) = 3, f′(1) = -8
67.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
1.571
0.7854
-0.7854
0
68.
A curve y = F(x) passes through (1, -2) and its gradient is the expression shown. Find y when x = 2.
A curve y = F(x) passes through (1, -2) and its gradient is the expression shown. Find y when x = 2.
0.7392
2.779
1.706
-0.2273
69.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
6.999
9.888
14
-6.999
70.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
5164
5184
2582
-2582
71.
A curve y = F(x) passes through (1, -2) and its gradient is the expression shown. Find y when x = 3.
A curve y = F(x) passes through (1, -2) and its gradient is the expression shown. Find y when x = 3.
15
18
21.33
14.67
72.
If f″(x) = 18⋅x + 10, f′(0) = -1 and f(0) = -4, which option is correct?
If f″(x) = 18⋅x + 10, f′(0) = -1 and f(0) = -4, which option is correct?
f(2) = 38, f′(2) = 55
f(2) = 38, f′(2) = 56
f(2) = 37, f′(2) = 55
f(2) = 56, f′(2) = -1
73.
A curve y = F(x) passes through (1, 6) and its gradient is the expression shown. Find y when x = 2.
A curve y = F(x) passes through (1, 6) and its gradient is the expression shown. Find y when x = 2.
-5.5
6.833
2
0.6667
74.
A curve y = F(x) passes through (1, -5) and its gradient is the expression shown. Find y when x = 3.
A curve y = F(x) passes through (1, -5) and its gradient is the expression shown. Find y when x = 3.
14.22
1.385
6.206
-1.806
75.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
82.34
60.26
41.17
-41.17
76.
A curve y = F(x) passes through (0, -3) and its gradient is the expression shown. Find y when x = 1.
A curve y = F(x) passes through (0, -3) and its gradient is the expression shown. Find y when x = 1.
-2.5
1
3.5
0.5
77.
A curve y = F(x) passes through (2, -4) and its gradient is the expression shown. Find y when x = 3.
A curve y = F(x) passes through (2, -4) and its gradient is the expression shown. Find y when x = 3.
36.47
21.09
9.696
23.09
78.
If f″(x) = 12 - 12⋅x, f′(0) = 1 and f(0) = 0, which option is correct?
If f″(x) = 12 - 12⋅x, f′(0) = 1 and f(0) = 0, which option is correct?
f(1) = 5, f′(1) = 1
f(1) = 5, f′(1) = 8
f(1) = 6, f′(1) = 7
f(1) = 5, f′(1) = 7
79.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
14.78
82.4
41.2
-41.2
80.
A curve y = F(x) passes through (0, 0) and its gradient is the expression shown. Find y when x = 2.
A curve y = F(x) passes through (0, 0) and its gradient is the expression shown. Find y when x = 2.
-1.01
1.99
4.99
2.291
81.
A curve y = F(x) passes through (0, 0) and its gradient is the expression shown. Find y when x = 1.
A curve y = F(x) passes through (0, 0) and its gradient is the expression shown. Find y when x = 1.
4.718
5.718
6.47
3.718
82.
Evaluate the definite integral shown (substitution or by parts).
Evaluate the definite integral shown (substitution or by parts).
0.8473
-0.8473
0.5714
1.695
83.
A curve y = F(x) passes through (2, 2) and its gradient is the expression shown. Find y when x = 3.
A curve y = F(x) passes through (2, 2) and its gradient is the expression shown. Find y when x = 3.
-3
-4.5
-0.5
-8.5
84.
A curve y = F(x) passes through (1, 6) and its gradient is the expression shown. Find y when x = 3.
A curve y = F(x) passes through (1, 6) and its gradient is the expression shown. Find y when x = 3.
-1.263
-1.004
-1.133
-6.222
85.
A curve y = F(x) passes through (0, 1) and its gradient is the expression shown. Find y when x = 1.
A curve y = F(x) passes through (0, 1) and its gradient is the expression shown. Find y when x = 1.
3.012
2
4.012
2.012
86.
If f″(x) = 12⋅x + 4, f′(0) = -4 and f(0) = -4, which option is correct?
If f″(x) = 12⋅x + 4, f′(0) = -4 and f(0) = -4, which option is correct?
f(2) = 32, f′(2) = 28
f(2) = 12, f′(2) = 28
f(2) = 8, f′(2) = -4
f(2) = 8, f′(2) = 28
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