Definite Integral
The base of a solid is a region in the first quadrant bounded by the x-axis, y-axis and the graph of the line x+2y=8, as shown in the figure below. If the cross sections of the solid perpendicular to the x-axis are semicircles, what is the volume of the solid?

Question

Definite Integral
The base of a solid is a region in the first quadrant bounded by the x-axis, y-axis and the graph of the line x+2y=8, as shown in the figure below.  If the cross sections of the solid perpendicular to the x-axis are semicircles, what is the volume of the solid?

precal · Answer

|dw:1405723341188:dw|

precal · Answer

$$\int\limits_{0}^{8}\frac{ \pi (4-\frac{ 1 }{ 2 }x)^2 }{ 2 }d$$

precal · Answer

I know my set up is incorrect

anonymous · Answer

I like drawing the regions for this problem with a tilted axis:
|dw:1405723788927:dw|