The area of the region bounded by the curve y | vedclass

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Question

(C) To find the area bounded by the curve $y = 2x - x^2$ and the $X$-axis,we first find the points of intersection with the $X$-axis by setting $y = 0

Vedclass · Accepted Answer

$\frac{4}{3}$

Vedclass · Answer

(C) To find the area bounded by the curve $y = 2x - x^2$ and the $X$-axis,we first find the points of intersection with the $X$-axis by setting $y = 0$.$2x - x^2 = 0$$x(2 - x) = 0$So,$x = 0$ and $x = 2$.The area $A$ is given by the integral of the curve from $x = 0$ to $x = 2$:$A = \int_{0}^{2} (2x - x^2) \, dx$$A = [x^2 - \frac{x^3}{3}]_{0}^{2}$$A = (2^2 - \frac{2^3}{3}) - (0^2 - \frac{0^3}{3})$$A = 4 - \frac{8}{3}$$A = \frac{12 - 8}{3} = \frac{4}{3}$ sq. units.

The area of the region bounded by the curve $y = 2x - x^2$ and the $X$-axis is . . . . . . sq. units.

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