The area of the region,bounded by the parabol | vedclass

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(D) The area of the region bounded by the curves $y=f(x)$ and $y=g(x)$ between $x=a$ and $x=b$ is given by $\int_a^b |f(x)-g(x)| dx$.Here,the region i

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$\frac{21}{2}$ sq. units

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(D) The area of the region bounded by the curves $y=f(x)$ and $y=g(x)$ between $x=a$ and $x=b$ is given by $\int_a^b |f(x)-g(x)| dx$.Here,the region is bounded by $y=x^2+2$ and $y=x$ from $x=0$ to $x=3$.Since $x^2+2 > x$ for all $x \in [0, 3]$,the required area is:$	ext{Area} = \int_0^3 (x^2+2-x) dx$$= \left[ \frac{x^3}{3} + 2x - \frac{x^2}{2} ight]_0^3$$= \left( \frac{3^3}{3} + 2(3) - \frac{3^2}{2} ight) - (0)$$= \left( \frac{27}{3} + 6 - \frac{9}{2} ight)$$= 9 + 6 - 4.5$$= 15 - 4.5 = 10.5 = \frac{21}{2} 	ext{ sq. units}$.

The area of the region,bounded by the parabola $y=x^2+2$ and the lines $y=x, x=0$ and $x=3$,is

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