The area bounded by the curve y=x^{3},the X-a | vedclass

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(D) The required area is given by the definite integral of the function $y=x^{3}$ from $x=1$ to $x=4$.$	ext{Area} = \int_{1}^{4} x^{3} dx$Using the p

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$\frac{255}{4}$ sq. units

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(D) The required area is given by the definite integral of the function $y=x^{3}$ from $x=1$ to $x=4$.$	ext{Area} = \int_{1}^{4} x^{3} dx$Using the power rule for integration,$\int x^{n} dx = \frac{x^{n+1}}{n+1}$,we get:$	ext{Area} = \left[\frac{x^{4}}{4}ight]_{1}^{4}$Now,apply the limits:$	ext{Area} = \frac{1}{4} [4^{4} - 1^{4}]$$	ext{Area} = \frac{1}{4} [256 - 1]$$	ext{Area} = \frac{255}{4} 	ext{ sq. units}$

The area bounded by the curve $y=x^{3}$,the $X$-axis and the lines $x=1$ and $x=4$ is

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