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8. Application and integration — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths8. Application and integration1 Mark
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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