Find the area under the given curve y=x^{2} b | vedclass

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(A) The required area is represented by the shaded region bounded by the curve $y=x^{2}$,the lines $x=1$,$x=2$,and the $x$-axis.The area is given by t

Vedclass · Accepted Answer

$\frac{7}{3}$ sq. units

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(A) The required area is represented by the shaded region bounded by the curve $y=x^{2}$,the lines $x=1$,$x=2$,and the $x$-axis.The area is given by the definite integral:$	ext{Area} = \int_{1}^{2} y \, dx$Substituting $y = x^{2}$:$	ext{Area} = \int_{1}^{2} x^{2} \, dx$Evaluating the integral:$	ext{Area} = \left[ \frac{x^{3}}{3} ight]_{1}^{2}$Applying the limits:$	ext{Area} = \left( \frac{2^{3}}{3} ight) - \left( \frac{1^{3}}{3} ight)$$	ext{Area} = \frac{8}{3} - \frac{1}{3}$$	ext{Area} = \frac{7}{3} 	ext{ sq. units}$

Find the area under the given curve $y=x^{2}$ bounded by the lines $x=1$,$x=2$ and the $x$-axis.

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