Revision Test 12
This Revision Test covers the material contained in Chapters 40 to 42. The marks for each question are shown in
brackets at the end of each question.
1. Determine the following integrals:
(a)
cos
3 x sin
2 x dx (b)
2
(9 − 4x 2 )
dx
(c)
2
(4x 2 − 9)
dx
(14)
2. Evaluate the following definite integrals, correct to
4 significant figures:
(a)
π
2
0
3 sin
2 t dt (b)
π
3
0
3 cos5θ sin 3θ dθ
(c)
2
0
5
4 + x 2 dx
(15)
3. Determine:
(a)
x − 11
x 2 − x − 2
dx
(b)
3 − x
(x 2 + 3)(x + 3)
dx
(21)
4. Evaluate
2
1
3
x 2 (x + 2)
dx correct to 4 significant
figures.
(12)
5. Determine:
dx
2 sin x + cos x
(8)
6. Evaluate
π
2
π
3
dx
3 − 2 sin x
correct to 3 decimal
places.
(10)
This Revision Test covers the material contained in Chapters 40 to 42. The marks for each question are shown in
brackets at the end of each question.
1. Determine the following integrals:
(a)
cos
3 x sin
2 x dx (b)
2
(9 − 4x 2 )
dx
(c)
2
(4x 2 − 9)
dx
(14)
2. Evaluate the following definite integrals, correct to
4 significant figures:
(a)
π
2
0
3 sin
2 t dt (b)
π
3
0
3 cos5θ sin 3θ dθ
(c)
2
0
5
4 + x 2 dx
(15)
3. Determine:
(a)
x − 11
x 2 − x − 2
dx
(b)
3 − x
(x 2 + 3)(x + 3)
dx
(21)
4. Evaluate
2
1
3
x 2 (x + 2)
dx correct to 4 significant
figures.
(12)
5. Determine:
dx
2 sin x + cos x
(8)
6. Evaluate
π
2
π
3
dx
3 − 2 sin x
correct to 3 decimal
places.
(10)