9. Graphical Applications of Integrals

9–20. Arc length calculations Find the arc length of the following curves on the given interval.

x = y⁴/4 + 1/8y², for 1≤y≤2

42-47. Volumes of Solids Find the volume of the solid generated when the given region is revolved as described.

44. The region bounded by f(x) = sin(x) and the x-axis on [0, π] is revolved about the y-axis.

Find the volume of the solid whose base is the region bounded by the function $f\left(x\right)=\sqrt{9-x^2}$ and the x-axis with square cross sections perpendicular to the x-axis.

Find the volume for a solid whose base is the region between the curve $y=\sqrt{\sin x}$ and the x-axis on the interval from $[0,\pi ]$ and whose cross sections are equilateral triangles with bases parallel to the y-axis.

Find the volume of the solid obtained by rotating the region bounded by $y=x+4$, $y=0$, $x=1$ & $x=5$ about the x-axis.

Find the volume of the solid formed by revolving the area bounded by $f\left(x\right)=x^2$ from $x=0$ to $x=3$ and the y-axis around the y-axis.

74. Volume of a Solid

Consider the region R bounded by:

The graph of f(x) = 1/(x + 2)

The x-axis on the interval [0,3].

Find the volume of the solid formed when R is revolved about the y-axis.

Let f(x) = √(x + 1). Find the area of the surface generated when:

Region bounded by f(x) and the x-axis on [0, 1]

Revolved about the x-axis