Revision Test 11
This Revision Test covers the material contained in Chapters 37 to 39.The marks for each question are shown in
brackets at the end of each question.
- Determine: (a)
∫
3√
t^5 dt (b)∫
2√ (^3) x 2 dx
(c)
∫
( 2 +θ)^2 dθ (9)
- Evaluate the following integrals, each correct to
4 significant figures:
(a)∫ π
3
03sin2tdt (b)∫ 21(
2
x^2+1
x+3
4)
dx(c)∫ 103
e^2 tdt (15)- Calculate the area between the curve
y=x^3 −x^2 − 6 xand thex-axis. (10) - A voltagev=25sin50πtvolts is applied across
an electrical circuit. Determine, using integration,
its mean and r.m.s. values over the ranget=0to
t=20ms, each correct to 4 significant figures.
(12) - Sketch on the same axes the curvesx^2 = 2 yand
y^2 = 16 x and determine the co-ordinates of the
points of intersection. Determine (a) the area
enclosed by the curves, and (b) the volume of the
solid produced if the area is rotated one revolution
about thex-axis. (13) - Calculate the position of the centroid of the
sheet of metal formed by thex-axis and the part of
the curvey= 5 x−x^2 which lies above thex-axis.
(9) - A cylindrical pillar of diameter 400mm has a
groove cut around its circumference as shown in
Fig. RT11.1. The section of the groove is a semi-
circle of diameter 50mm. Given that the centroid
of a semicircle from its base is
4 r
3 π,usethetheorem of Pappus to determine the volume of
material removed, in cm^3 , correct to 3 significant
figures. (8)400 mm200 mm50 mmFigure RT11.1- A circular door is hinged so that it turns about
a tangent. If its diameter is 1.0m find its second
moment of area and radius of gyration about the
hinge. (5) - Determine the following integrals:
(a)∫
5 ( 6 t+ 5 )^7 dt (b)∫
3lnx
xdx(c)∫
2
√
( 2 θ− 1 )dθ (9)- Evaluate the following definite integrals:
(a)∫ π
2
02sin(
2 t+π
3)
dt (b)∫ 103 xe^4 x(^2) − 3
dx
(10)