Area Under The Curves - Calculus - Mathematics Previous Year Questions

The area (in sq units) bounded by the curve $y=2 x-x^2$ and the line $y=-x$ is

Area of the region bounded by the curve $y=2-x-3 x^2$, the $X$-axis, the $Y$-axis and the line $x=-2$ is

The area (in sq units) of the region bounded by the circle $x^2+y^2=64$, positive $X$-axis and the line $y=\sqrt{3} x$ is

The area (in sq units) of the region bounded by the curve $y=|\sin 2 x|$ and the $X$-axis in $[0,2 \pi]$ is

The area (in square units) of the region enclosed between the parabola $y^2=2 x$ and the line $y=4 x-1$

If the area of the region bounded by $y=\cos x, y=\sin x$, $x=\pi / 4$ and $x=\pi$ is bisected by the line $x=a$, then $\sin \left(a+\frac{\pi}{4}\right)=$