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

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(D) The given equation is $y = 2 \sqrt{1 - x^2}$.Squaring both sides,we get $y^2 = 4(1 - x^2)$,which implies $x^2 + \frac{y^2}{4} = 1$.This is the equ

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$\pi$

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(D) The given equation is $y = 2 \sqrt{1 - x^2}$.Squaring both sides,we get $y^2 = 4(1 - x^2)$,which implies $x^2 + \frac{y^2}{4} = 1$.This is the equation of an ellipse with semi-major axis $a = 2$ (along the $Y$-axis) and semi-minor axis $b = 1$ (along the $X$-axis).Since the curve is $y = 2 \sqrt{1 - x^2}$,it represents the upper half of the ellipse.The area bounded by the curve and the $X$-axis is the area of the upper semi-ellipse.The area of the full ellipse is given by $A = \pi ab = \pi 	imes 1 	imes 2 = 2 \pi$.Therefore,the area of the upper semi-ellipse is $\frac{1}{2} 	imes 2 \pi = \pi$ sq. units.

The area of the region bounded by the curve $y = 2 \sqrt{1 - x^2}$ and the $X$-axis is . . . . . . sq. units.

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