# Q : 3         Find the area of the region bounded by the curves  $\dpi{100} \small y=x^2+2,y=x,x=0$ and $\dpi{100} \small x=3$.

D Divya Prakash Singh

The area of the region bounded by the curves,

$\dpi{100} \small y=x^2+2,y=x,x=0$ and $\dpi{100} \small x=3$ is represented by the shaded area OCBAO as

Then, Area OCBAO will be = Area of ODBAO - Area of ODCO

which is equal to

$\int_0^3(x^2+2)dx - \int_0^3x dx$

$= \left ( \frac{x^3}{3}+2x \right )_0^3 -\left ( \frac{x^3}{2} \right )_0^3$

$= \left [ 9+6 \right ] - \left [ \frac{9}{2} \right ] = 15-\frac{9}{2} = \frac{21}{2}units.$

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