Higher Engineering Mathematics

Assign-12-H8152.tex 23/6/2006 15: 12 Page 441

H

Integral calculus

Assignment 12

This assignment covers the material contained

in Chapters 43 to 45.

The marks for each question are shown in

brackets at the end of each question.

1. Determine the following integrals:

(a)

∫

5 xe^2 xdx (b)

∫

t^2 sin 2tdt (13)

2. Evaluate correct to 3 decimal places:
   ∫ 4

1

√

xlnxdx (10)

3. Use reduction formulae to determine:

(a)

∫

x^3 e^3 xdx (b)

∫

t^4 sintdt (13)

4. Evaluate

∫ π

2

0

cos^6 xdx using a reduction

formula. (6)

5. Evaluate

∫ 3

1

5

x^2

dxusing (a) integration (b) the

trapezoidal rule (c) the mid-ordinate rule

(d) Simpson’s rule. In each of the approximate

methods use 8 intervals and give the answers

correct to 3 decimal places. (19)

6. An alternating currentihas the following values
   at equal intervals of 5 ms:

Timet(ms) 0 5 10 15 20 25 30

Currenti(A) 0 4.8 9.1 12.7 8.8 3.5 0

Chargeq, in coulombs, is given by

q=

∫ 30 × 10 − 3

0 idt.

Use Simpson’s rule to determine the approximate

charge in the 30 ms period. (4)