Volume of Solids

• Apr 27th 2009, 04:41 PM
summermagic
Volume of Solids
Let f and g be the functions given by $\displaystyle f(x)=1+sin(2x)$ and $\displaystyle g(x)=e^{x/2}$. Let R be the shaded region in the first quadrant enclosed by the graphs of f and g.

The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles with diameters extending from y=f(x) to y=g(x). Find the volume of this solid.

How do I do this problem?
• Apr 27th 2009, 06:26 PM
skeeter
Quote:

Originally Posted by summermagic
Let f and g be the functions given by $\displaystyle f(x)=1+sin(2x)$ and $\displaystyle g(x)=e^{x/2}$. Let R be the shaded region in the first quadrant enclosed by the graphs of f and g.

The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles with diameters extending from y=f(x) to y=g(x). Find the volume of this solid.

How do I do this problem?

$\displaystyle A = \frac{\pi}{2} r^2$

$\displaystyle r = \frac{f(x) - g(x)}{2}$

$\displaystyle V = \int_a^b A(x) \, dx$