# Integration, Long Questions (Question 6)

Question 6:
Diagram below shows part of the curve  $y=\frac{2}{{\left(3x-2\right)}^{2}}$  which passes through (1, 2).

(a)   Find the equation of the tangent to the curve at the point B.
(b)  A region is bounded by the curve, the x-axis and the straight lines x = 2 and x = 3.
(i) Find the area of the region.
(ii) The region is revolved through 360° about the x–axis. Find the volume generated,
in terms of p.

Solution:
(a)

(b)(i)

(b)(ii)