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Application of Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsApplication of Definite Integration2 Marks
MCQ
Area lying between the curves $y^2=2 x$ and $y=x$ is
  • A
    $\frac{1}{3}$ sq. units
  • B
    $\frac{3}{4}$ sq. units
  • ✓
    $\frac{2}{3}$ sq. units
  • D
    $\frac{1}{4}$ sq. units
✓

Answer

Correct option: C.
$\frac{2}{3}$ sq. units
(C)
Here, $a =\frac{1}{2}$ and $m =1$
The area of the region bounded by $y^2=4 a x$ and $y= m x$ is $\frac{8 a ^2}{3 m^3}$ sq. units.
$\therefore$ Required area $=\frac{8\left(\frac{1}{2}\right)^2}{3(1)^3}=\frac{2}{3}$ sq. units

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