Cambridge International AS and A Level Mathematics Pure Mathematics 1

Integration

P1^

6

8  The diagram shows part of the curve y a

x

= , where a is a positive constant.

    Given that the volume obtained when the shaded region is rotated through

360° about the x axis is    24 π, find the value of a.

[Cambridge AS & A Level Mathematics 9709, Paper 12 Q2 June 2010]

y

O^13 x

y =ax

KEY POINTS

1  d

d

y

x

xyn nx c

n

= = + +

+ 1

⇒ 1                  n ≠ –1

2    xx x

n

ba

n

n n

a

b

a

b nn

d =

+









=

+

+ + +

∫

1 1 1

11

• n ≠ –1

3  Area A =

=

∫

∫

yx

xx

a

b

a

b

d

fd()

y

O a b x

y = f(x)

A