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)
5x e
2x dx
(b)
t
2 sin 2t dt
(13)
2. Evaluate correct to 3 decimal places:
4
1
√
x ln x dx
(10)
3. Use reduction formulae to determine:
(a)
x
3 e
3x dx
(b)
t
4 sin t dt
(13)
4. Evaluate
π
2
0
cos
6 x dx 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 approximate methods use 8 intervals and give the answers
correct to 3 decimal places.
(19)
6. An alternating current i has the following values at
equal intervals of 5 ms:
Time t (ms) 0 5 10 15 20 25 30
Current i(A) 0 4.8 9.1 12.7 8.8 3.5 0
Charge q, in coulombs, is given by
q =
30×10 −3
0
i dt .
Use Simpson’s rule to determine the approximate
charge in the 30 ms period.
(4)
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)
5x e
2x dx
(b)
t
2 sin 2t dt
(13)
2. Evaluate correct to 3 decimal places:
4
1
√
x ln x dx
(10)
3. Use reduction formulae to determine:
(a)
x
3 e
3x dx
(b)
t
4 sin t dt
(13)
4. Evaluate
π
2
0
cos
6 x dx 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 approximate methods use 8 intervals and give the answers
correct to 3 decimal places.
(19)
6. An alternating current i has the following values at
equal intervals of 5 ms:
Time t (ms) 0 5 10 15 20 25 30
Current i(A) 0 4.8 9.1 12.7 8.8 3.5 0
Charge q, in coulombs, is given by
q =
30×10 −3
0
i dt .
Use Simpson’s rule to determine the approximate
charge in the 30 ms period.
(4)