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

y=x^2-5 x, y=7 x-x^2 \ => x^2-5 x=7 x-x^2 \ => x=0, x=6 Area = integral _0^6 [ (7x - x^2) - (x - 5x) ] dx \ = integral _0^6 (12x - 2x^2) dx \ = [ 6x - (2x^3 / 3) ]_0^6 =216-144=72 sq. unit But answer is 198 as per NTA.

The area of the region enclosed by the parabolas yx25 x... | (Mathematics)

$y=x^2-5 x, y=7 x-x^2 \\ \Rightarrow \quad x^2-5 x=7 x-x^2 \\ \Rightarrow \quad x=0, x=6$

$\begin{aligned} \text{Area} &= \int_{0}^{6} \left[ \left(7x - x^2\right) - (x - 5x) \right] dx \\ &= \int_{0}^{6} \left(12x - 2x^2\right) dx \\ &= \left[ 6x - \frac{2x^3}{3} \right]_{0}^{6} \end{aligned}$

$=216-144=72 \text { sq. unit }$

But answer is 198 as per NTA.

Explanation

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