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

Question

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

Answer: 198

Accepted Answer

$\begin{gathered} y={x}^{2}-5x,y=7x-{x}^{2} \Rightarrow \, {x}^{2}-5x=7x-{x}^{2} \ \Rightarrow \, x=0,x=6 \end{gathered}$

$=\int _{0}^{6}[(7x-{x}^{2})-(x-5x)]dx$

$=\int _{0}^{6}(12x-2{x}^{2})dx=6x-{\frac{2{x}^{3}}{3}|}_{6}^{0}$

$=216-144=72$

But answer is 198 as per NTA.

Solutions · 1