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

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Question

(D) The area $A$ bounded by the curve $y = f(x)$,the $x$-axis,and the lines $x = a$ and $x = b$ is given by the integral $A = \int_{a}^{b} |f(x)| dx$.

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) The area $A$ bounded by the curve $y = f(x)$,the $x$-axis,and the lines $x = a$ and $x = b$ is given by the integral $A = \int_{a}^{b} |f(x)| dx$.Here,$f(x) = x^3$,$a = 1$,and $b = 4$.Since $x^3 > 0$ for $x \in [1, 4]$,the area is:$A = \int_{1}^{4} x^3 dx$$A = \left[ \frac{x^4}{4} ight]_{1}^{4}$$A = \frac{4^4}{4} - \frac{1^4}{4}$$A = \frac{256}{4} - \frac{1}{4}$$A = \frac{255}{4} 	ext{ sq. units}$.Thus,the correct option is $D$.

The area bounded by the curve $y = x^3$,the $x$-axis,and the ordinates $x = 1$ and $x = 4$ is:

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