volume of the solid

[kapplayer]

I'm have trouble wit thish problem im not sure how to do it: find the volume of the solid whose base is bounded by the graph of y=e^x ,-infinity<x<=ln2, with cross sectionn perpendicular to the x-axis are circular disks with diameters reaching from the x-axis to the curve.
Thanks for your help

 

[galactus]

Do you mean the cross sections are semicircles perp. to the x-axis?. That woud make more sense.

The radius of each semicircle would be \(\displaystyle y=\frac{e^{x}}{2}\)

The area of each semicircle would be \(\displaystyle \frac{\pi}{2}y^{2}\)

Now, can you put it together and integrate?.

 

[kapplayer]

so it would 2pie the integral from -infinity to ln2 x(e^x)dx but what do i do with

 

[galactus]

'pie'?. Please don't do that. :roll:

Note: this is not a volume of revolution. It is counting up the cross-sectional area of the semi-circles.