Mathematics · Area under the Curves

JEE Main 2024 — 5 April, Shift 1 — Question 23

The area of the region enclosed by the parabolas $y=x^{2}-5 x$ and $y=7 x-x^{2}$ is $\_\_\_\_\_\_\_\_$

Answer: 72

Numerical answer — enter this value.

$y=x^{2}-5 x$ and $y=7 x-x^{2}$

$\int_{0}^{6}(\mathrm{~g}(\mathrm{x})-\mathrm{f}(\mathrm{x})) \mathrm{dx}$

$\int_{0}^{6}\left(\left(7 x-x^{2}\right)-\left(x^{2}-5 x\right)\right) d x$

$\int_{0}^{6}\left(12 x-2 x^{2}\right) d x=\left[12 \frac{x^{2}}{2}-\frac{2 x^{3}}{3}\right]_{0}^{6}$ $\Rightarrow 6(6)^{2}-\frac{2}{3}(6)^{3}$

$=216-144=72$ unit $^{2}$

Answer key and solution verified before publishing.

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