Search any question & find its solution
Question:
Answered & Verified by Expert
Area bounded between the curve $x^{2}=y$ and the line $y=4 x$ is
Options:
Solution:
2183 Upvotes
Verified Answer
The correct answer is:
$\frac{32}{3} \mathrm{sq}$ unit
Given curves are $x^{2}=y$ and $y=4 x$
Intersection points are $(0,0)$ and $(4,16)$ $\begin{aligned} \therefore \text { Required area } &=\int_{0}^{4}\left(4 x-x^{2}\right) d x \\ &=\left[\frac{4 x^{2}}{2}-\frac{x^{3}}{3}\right]_{0}^{4} \\ &=\left[32-\frac{64}{3}\right] \\ &=\frac{32}{3} \mathrm{sq} \text { unit } \end{aligned}$
Intersection points are $(0,0)$ and $(4,16)$ $\begin{aligned} \therefore \text { Required area } &=\int_{0}^{4}\left(4 x-x^{2}\right) d x \\ &=\left[\frac{4 x^{2}}{2}-\frac{x^{3}}{3}\right]_{0}^{4} \\ &=\left[32-\frac{64}{3}\right] \\ &=\frac{32}{3} \mathrm{sq} \text { unit } \end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.