The area (in sq. units) of the region bounded by the curve $y = 2x - x^2$ and the $X$-axis is...

The area in square units of the region bounded by the curve $y = \sqrt{16 - x^2}$ and the lines $x = 0, x = 4$ above the $X$-axis is: (in $\pi$)

The area of the region bounded by the parabola $y^2 = 27x$ and the line $x = 1$ is . . . . . . sq. units. (in $\sqrt{3}$)

If $f(x) = x + e^x$,then the area bounded by $f^{-1}(x)$,the ordinates $x = 1$ and $x = 1 + e$,and the $x$-axis is (in $sq. units$):

Using integration,find the area of the triangular region whose sides have the equations $y=2x+1$,$y=3x+1$,and $x=4$.

$A$ frustum of a sphere is made by cutting a sphere with two parallel planes. If the radius of the sphere is $5 \, cm$ and the distance between the planes is $1 \, cm$,what is the curved surface area of the frustum when the distance of the first plane from the center of the sphere is $2 \, cm$?