Higher Engineering Mathematics, Sixth Edition

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 xsin^2 xdx (b)

∫

2

√

( 9 − 4 x^2 )

dx

(c)

∫

2

√

( 4 x^2 − 9 )

dx (14)

2. Evaluate the following definite integrals, correct to
   4 significant figures:

(a)

∫ π

2

0

3sin^2 tdt (b)

∫ π

3

0

3cos5θsin3θdθ

(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 )

dxcorrect to 4 significant

figures. (12)

5. Determine:

∫

dx

2sinx+cosx

(8)

6. Evaluate

∫ π 2

π

3

dx

3 −2sinx

correct to 3 decimal

places. (10)