Volume of Solids

**summermagic** · April 27th 2009, 04:41 PM

Let f and g be the functions given by $f(x)=1+sin(2x)$ and $g(x)=e^{x/2}$ . 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?

**skeeter** · April 27th 2009, 06:26 PM

Originally Posted by summermagic

Let f and g be the functions given by $f(x)=1+sin(2x)$ and $g(x)=e^{x/2}$ . 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?

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

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

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

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