ABSTRACT

This Revision test covers the material contained in Chapters 51 to 53. 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 3sin 2t dt

(b) ∫ 2

( 2 x2

+ 1 x

+ 3 4

) dx (10)

3. Determine the following integrals:

(a) ∫

5(6t + 5)7dt

(b) ∫ 3ln 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 3sin2 t dt

(b) ∫ π/3

0 3cos5θ sin 3θ dθ

(c) ∫ 2

5 4 + x2 dx (14)

For lecturers/instructors/teachers, fully worked solutions to each of the problems in Revision Test 15, together with a full marking scheme, are available at the website:

www.routledge.com/cw/bird