(B) The area bounded by the curve $y^2 = x$,the line $y = 4$,and the $y$-axis is given by the integral with respect to $y$.Since $y^2 = x$,we have $x

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(B) The area bounded by the curve $y^2 = x$,the line $y = 4$,and the $y$-axis is given by the integral with respect to $y$.Since $y^2 = x$,we have $x = y^2$.The limits for $y$ are from $0$ to $4$.Required Area $= \int_{0}^{4} x \, dy = \int_{0}^{4} y^2 \, dy$$= \left[ \frac{y^3}{3} \right]_{0}^{4}$$= \frac{4^3}{3} - \frac{0^3}{3} = \frac{64}{3}$ square units.

Class 12 Mathematics Application of Integration Area bounded by region of single curve

Medium

The area bounded by the curve $y^2 = x$,the line $y = 4$,and the $y$-axis is

A
$\frac{16}{3}$
B
$\frac{64}{3}$
C
$7\sqrt{2}$
D
None of these

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Application of Integration

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Area bounded by region of single curve

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The area bounded by the curve $y^2 = x$,the line $y = 4$,and the $y$-axis is

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