Higher Engineering Mathematics

Assign-11-H8152.tex 23/6/2006 15: 12 Page 417

H

Integral calculus

Assignment 11

This assignment 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

√

(4x^2 −9)

dx (14)

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

(a)

∫ π

2

0

3 sin^2 tdt (b)

∫ π

3

0

3 cos 5θsin 3θdθ

(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

2 sinx+cosx

(8)

6. Evaluate:

∫π

2

π

3

dx

3 −2 sinx

correct to 3 decimal

places. (10)