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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths8. Application and integration1 Mark
MCQ
Area bounded by parabola ${y^2} = x$ and straight line $2y = x$ is
  • ✓
    $\frac{4}{3}$
  • B
    $1$
  • C
    $\frac{2}{3}$
  • D
    $\frac{1}{3}$
✓

Answer

Correct option: A.
$\frac{4}{3}$
a
(a) ${y^2} = x$ and $2y = x $

$\Rightarrow {y^2} = 2y \Rightarrow y = 0,\,2$

$\therefore \,$ Required area $ = \int_0^2 {({y^2} - 2y)dy = \left( {\frac{{{y^3}}}{3} - {y^2}} \right)_0^2}$

$={ \frac{4}{3}}  \,\, sq. \,unit$.

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