Practicing Success
Area bounded between the parabola $y=x^2-2$ and the line $y=x$ in square units is : |
$\frac{9}{2}$ $\frac{11}{2}$ $\frac{7}{2}$ 5 |
$\frac{9}{2}$ |
The correct answer is Option (1) → $\frac{9}{2}$ $y=x^2-2$ $y=x$ so $x=x^2-2$ so $x=-1,2$ $y=-1,2$ shifting indices to make calculations simplar let $X=x,Y=y+2$ so new eq. $Y-2=X^2-2$ $Y=X^2$ ...(1) for line $Y-2=X$ or $Y=X+2$ ...(2) area required = $\int\limits_{-1}^2X+2-X^2dx$ $=\left[\frac{X^2}{2}+2X-\frac{X^3}{3}\right]_{-1}^2$ $=2+4-\frac{8}{3}-\frac{1}{2}+2-\frac{1}{3}=8-\frac{1}{2}-3=5-\frac{1}{2}$ $=\frac{9}{2}$ sq. units |