The area of the region left{(x, y): x^2 leq y | vedclass

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Question

$y \geq x^2 \quad y \leq 8-x^2 \quad y \leq 7$

$x^2=8-x^2$

$x^2=4$

$x= \pm 2$

$2\left(1.7+\int \limits_1^2\left(8-2 x^2\right) d x\right)-

Vedclass · Accepted Answer

$20$

Vedclass · Answer

$y \geq x^2 \quad y \leq 8-x^2 \quad y \leq 7$

$x^2=8-x^2$

$x^2=4$

$x= \pm 2$

$2\left(1.7+\int \limits_1^2\left(8-2 x^2\right) d x\right)-2 \int \limits_0^1\left(x^2\right) d x$

$=2\left[7+\left(8 x-\frac{2 x^3}{3}\right)_1^2\right]-2\left(\frac{x^3}{3}\right)_0^1$

$=2\left[7+\left(16-\frac{16}{3}\right)-\left(8-\frac{2}{3}\right)\right]-2\left(\frac{1}{3}\right)$

$=2\left[7+\frac{32}{3}-\frac{22}{3}\right]=2\left[7+\frac{10}{3}\right] \frac{-2}{3}$

$=\frac{60}{3}=20$

The area of the region $\left\{(x, y): x^2 \leq y \leq 8-x^2, y \leq 7\right\}$ is

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