Application of Integrals

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?