The area (in square units) of the region boun | vedclass

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(C) The given equations are:$x^2 = 8y$  $(i)$$x = 4$  (ii)$y = 0$ (the $X$-axis)  (iii)From equation $(i)$, we have $y = \frac{x^2}{8}$.The region is

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$\frac{8}{3}$

Vedclass · Answer

(C) The given equations are:$x^2 = 8y$  $(i)$$x = 4$  (ii)$y = 0$ (the $X$-axis)  (iii)From equation $(i)$, we have $y = \frac{x^2}{8}$.The region is bounded by the parabola $x^2 = 8y$, the line $x = 4$, and the $X$-axis from $x = 0$ to $x = 4$.The required area $A$ is given by:$A = \int_{0}^{4} y \, dx$$A = \int_{0}^{4} \frac{x^2}{8} \, dx$$A = \frac{1}{8} \left[ \frac{x^3}{3} ight]_{0}^{4}$$A = \frac{1}{8} \left( \frac{4^3}{3} - \frac{0^3}{3} ight)$$A = \frac{1}{8} \left( \frac{64}{3} ight)$$A = \frac{8}{3} 	ext{ square units}$.

The area (in square units) of the region bounded by $x^2=8y$, $x=4$ and the $X$-axis is:

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