ABSTRACT
This Revision test covers the material contained in Chapters 48 to 50. The marks for each question are shown in brackets at the end of each question. 1. Determine:
(a) ∫
3 √
t5 dt
(b) ∫ 2
3√ x2
dx
(c) ∫
(2 + θ)2dθ (9)
2. Evaluate the following integrals, each correct to 4 significant figures:
(a) ∫ π/3
0 3 sin 2t dt
(b) ∫ 2
( 2 x2
+ 1 x
+ 3 4
) dx (10)
3. Determine the following integrals:
(a) ∫
5(6t + 5)7dt
(b) ∫ 3 ln x
x dx
(c) ∫ 2√(2θ − 1) dθ (9)
4. Evaluate the following definite integrals:
(a) ∫ π/2
0 2 sin
( 2t + π
) dt
(b) ∫ 1
5. Determine the following integrals:
(a) ∫
cos3 x sin2 x dx
(b) ∫ 2√
9 − 4x2 dx (8)
6. Evaluate the following definite integrals, correct to 4 significant figures:
(a) ∫ π/2
0 3 sin2 t dt
(b) ∫ π/3
0 3 cos 5θ sin 3θ dθ
(c) ∫ 2
5 4 + x2 dx (14)
