Question 1018

Definite Integrals: Areas and Volumes

2018 Paper 1 Question 2 Variant

Question

Do not use a calculator in answering this question.

A curve has equation $y = \frac{2}{x}$ and a line has equation ${3 y + 4 x=14.}$ The curve and the line intersect at the points ${A}$ and ${B.}$

(i)

Find the

{x}

-coordinates of

{A}

and

{B.}

[2]

(ii)

Find the exact volume generated when the area bounded by the curve and the line is rotated about the

{x\textrm{-axis}}

through

{360^\circ.}

[4]