The area (in square units) of the region boun | vedclass

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(B) 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,$f(x) = x^2+

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$\frac{15}{2}$

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(B) 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,$f(x) = x^2+2$ and $g(x) = x+1$ for $x \in [0, 3]$.Since $x^2+2 \ge x+1$ for all $x \in [0, 3]$,the required area is:$Area = \int_0^3 \{(x^2+2)-(x+1)\} dx$$Area = \int_0^3 (x^2-x+1) dx$$Area = \left[ \frac{x^3}{3} - \frac{x^2}{2} + x \right]_0^3$$Area = \left( \frac{3^3}{3} - \frac{3^2}{2} + 3 \right) - 0$$Area = \left( 9 - \frac{9}{2} + 3 \right) = 12 - 4.5 = 7.5 = \frac{15}{2}$ square units.

The area (in square units) of the region bounded by the parabola $y=x^2+2$ and the lines $y=x+1$,$x=0$,and $x=3$ is:

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