Area of the region bounded by the curve y^{2} | vedclass

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Question

(B) The area bounded by the curve $y^{2}=4x$,the $y$-axis,and the line $y=3$ is calculated by integrating $x$ with respect to $y$ from $y=0$ to $y=3$.

Vedclass · Accepted Answer

$\frac{9}{4}$

Vedclass · Answer

(B) The area bounded by the curve $y^{2}=4x$,the $y$-axis,and the line $y=3$ is calculated by integrating $x$ with respect to $y$ from $y=0$ to $y=3$.Given the curve $y^{2}=4x$,we can express $x$ as $x = \frac{y^{2}}{4}$.The area $A$ is given by the integral:$A = \int_{0}^{3} x \, dy$Substituting $x = \frac{y^{2}}{4}$:$A = \int_{0}^{3} \frac{y^{2}}{4} \, dy$$A = \frac{1}{4} \left[ \frac{y^{3}}{3} ight]_{0}^{3}$$A = \frac{1}{4} \left( \frac{3^{3}}{3} - \frac{0^{3}}{3} ight)$$A = \frac{1}{4} \left( \frac{27}{3} ight)$$A = \frac{1}{4} (9) = \frac{9}{4} 	ext{ sq. units}$.Thus,the correct answer is $B$.

Area of the region bounded by the curve $y^{2}=4x$,$y$-axis and the line $y=3$ is

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