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

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Aicharya · Accepted Answer

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

$\begin{aligned} & \int_0^6(g(x)-f(x)) d x \\ & \int_0^6\left(\left(7 x-x^2\right)-\left(x^2-5 x\right)\right) d x \\ & \int_0^6\left(12 x-2 x^2\right) d x=\left[12 \frac{x^2}{2}-\frac{2 x^3}{3}\right]_0^6 \\ & \Rightarrow 6(6)^2-\frac{2}{3}(6)^3 \\ & =216-144=72 \text { unit }^2 \\ & \end{aligned}$

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

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