Higher Engineering Mathematics, Sixth Edition

Revision Test 13

This Revision Test 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 sin2tdt (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

dx using (a) integration (b) the

trapezoidal rule (c) the mid-ordinate rule

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

mate 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 5ms:

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 30ms period. (4)