Q61 / 150 · MHT CET 2009 · Mathematics

Area bounded between the curve $x^{2}=y$ and the line $y=4 x$ is

  • Correct answer
    A
    $\frac{32}{3} \mathrm{sq}$ unit
  • B
    $\frac{1}{3} \mathrm{sq}$ unit
  • C
    $\frac{8}{3}$ sq unit
  • D
    $\frac{16}{3} \mathrm{sq}$ unit

Solution

Given curves are $x^{2}=y$ and $y=4 x$ Intersection points are $(0,0)$ and $(4,16)$ $\begin{aligned} \therefore \text { Required area } &=\int_{0}^{4}\left(4 x-x^{2}\right) d x \\ &=\left[\frac{4 x^{2}}{2}-\frac{x^{3}}{3}\right]_{0}^{4} \\ &=\left[32-\frac{64}{3}\right] \\ &=\frac{32}{3} \mathrm{sq} \text { unit } \end{aligned}$

Hence, the correct answer is option: 'A'.

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