Revision Test 11 : Volumes, irregular areas and volumes, and mean values 265
- Plot a graph ofy= 3 x^2 +5 fromx=1tox=4.
Estimate,correct to 2 decimal places,using 6 inter-
vals, the area enclosed by the curve, the ordinates
x=1andx=4, and thex-axis by
(a) the trapezoidal rule
(b) the mid-ordinate rule
(c) Simpson’s rule. (16) - A circular cooling tower is 20m high. The inside
diameter of the tower at different heights is given
in the following table.
Height (m) 0 5.0 10.0 15.0 20.0
Diameter (m) 16.0 13.3 10.7 8.6 8.0Determine the area corresponding toeach diame-
ter and hence estimate the capacity of the tower in
cubic metres. (7)- A vehicle starts from rest and its velocity is
measured every second for 6 seconds, with the
following results.
Timet(s) 0 1 2 3 4 5 6
Velocityv(m/s) 0 1.2 2.4 3.7 5.2 6.0 9.2Using Simpson’s rule, calculate
(a) the distance travelled in6s (i.e. the area under
thev/tgraph),
(b) the average speed over this period. (6)