The area bounded by the curve $y = -x^2$,the $x$-axis,$x = 1$,and $x = 4$ is:

The area bounded by the parabola $y^{2}=16x$ and its latus rectum in the first quadrant is

$A$ 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 $2 \, cm$?

Using integration,find the area of the region bounded by the triangle whose vertices are $(1, 0)$,$(2, 2)$,and $(3, 1)$.

Let $y = g(x)$ be the inverse of a bijective mapping $f : R \rightarrow R$ defined by $f(x) = 3x^3 + 2x$. The area bounded by the graph of $g(x)$,the $x-$axis,and the ordinate at $x = 5$ is:

The area bounded by the curve $y=x^{3}$,the $x$-axis,and the ordinates $x=-2$ and $x=1$ is