The area of the region bounded by the curve y | vedclass

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(B) The area $A$ of the region 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

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$\frac{10}{3}$ sq. units

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(B) The area $A$ of the region 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,$f(x) = x^{2}+1$,$a=1$,and $b=2$.Therefore,the area is:$A = \int_{1}^{2} (x^{2}+1) dx$$A = \left[ \frac{x^{3}}{3} + x ight]_{1}^{2}$$A = \left( \frac{2^{3}}{3} + 2 ight) - \left( \frac{1^{3}}{3} + 1 ight)$$A = \left( \frac{8}{3} + 2 ight) - \left( \frac{1}{3} + 1 ight)$$A = \left( \frac{8+6}{3} ight) - \left( \frac{1+3}{3} ight)$$A = \frac{14}{3} - \frac{4}{3}$$A = \frac{10}{3} 	ext{ sq. units}$

The area of the region bounded by the curve $y=x^{2}+1$,the lines $x=1, x=2$ and the $X$-axis is

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