### Application of Integrals

goals
The triangle formed by the tangent to the curve $f\left(x\right)={x}^{2}+bx-b$ at the point $\left(1,1\right)$ and the co-ordinate axes, lies in the first quadrant.If its area is $2$ sq.unit, then the value of $b$ is:
Find the area bounded by the curve $y=x|x|$, X-axis and the ordinates $x=-3$ and $x=3$.
A point P moves in xy-plane In such a way that [|x|] + [|y|] = 1 were [.] denotes the greatest integer function. Area of the region representing all possible positions of the point 'P' is equal to
For which of the following values of $m$, is the area of the region bounded by the curve $y=x-{x}^{2},$ and the line $y=mx$ equals $\dfrac{9}{2}$.sq.unit?
The area of bounded by the curve $y=log x$, the x-axis and the line $x=e$ is?