The area bounded by the curves y^2 = 8x and y = x is - Vidyadip

MCQ

The area bounded by the curves ${y^2} = 8x$ and $y = x$ is

A
$\frac{{128}}{3}\,\, sq. \,unit$
✓
$\frac{{32}}{3}\,\, sq. \,unit$
C
$\frac{{64}}{3}\,\, sq. \,unit$
D
$32\,\, sq. \,unit$

✓

Answer

Correct option: B.

$\frac{{32}}{3}\,\, sq. \,unit$

b
(b) ${y^2} = 8x$ and $y = x $

$\Rightarrow {x^2} = 8x \Rightarrow x = 0$,8

$\therefore$ Required area =$\int_0^8 {(2\sqrt 2 \sqrt x - x)dx} $

$ = \left[ {\frac{{4\sqrt 2 }}{3}{x^{3/2}} - \frac{{{x^2}}}{2}} \right]_0^8 $

$= \frac{{128}}{3} - \frac{{64}}{2} = \frac{{32}}{3}\,\, sq. \,unit$

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