Easiest
Region bounded by:
y=2,x=1,x=3,x-\text{axis}
\text{Rotated about the x-axis }
\int_1^3 4\pi dx
The region bounded by
y=2x+1, y-\text{axis}, x-\text{axis}, x=1
\text{Rotated about the x-axis}
\int_0^1 pi(2x+1)^2 dx
Region bounded by:
x=y^2 \text{ and } x=y
\text{Rotated about } y=-2
\int_0^1 2pi(y+2)(y-y^2)dy
\text{or}
\int_0^1 (pi(\sqrt(x)+2)^2-pi(x+2)^2)dx
Region bounded by
y=x^2-4 \text{ and } x-\text{axis}
\text{Rotated about } x=2
\int_-2^2 2pi(2-x)(4-x^2) dx
Region bounded by
y=e^x, y=x^2, x=2
\text{Rotated about x=4}
\int_{-.703}^2 2pi(4-x)(e^x-x^2)dx
Region bounded by:
x=2, x-\text{axis}, y-\text{axis}, y=3
\text{Rotated about the y-axis}
\int_0^3 4pi dy
Region bounded by
y=3-x, y-\text{axis}, x-\text{axis}
\text{Rotated about the x-axis}
\int_0^3 pi(3-x)^2 dx
Region bounded by
y=2x \text{ and} y=x^2
\text{Rotated about } y=-5
\int_0^2 2pi (x+5)(2x-x^2)dx
\text{or}
\int_0^4 ( pi (\sqrt{y}+5)^2 - \pi (\frac{y}{2}+5)^2 )dy
Region bounded by
y=x^2-4 \text{ and } y=12
\text{ Rotated about } y=12
\int_-4^4 pi(16-x^2)^2dx
The region bounded by
y=\sin(x) \text{ and } y=x^7
\text{Rotated about the line } x=-2
\int_{-.973}^0 2pi(x+2)(x^7-\sin(x))dx + \int_0^{.973} 2pi(x+2)(\sin(x)-x^7)dx