What is the volume of the solid of revolution generated by revolving R about the x-axis?
Let f(x) = e^(-3x/2)
Let R be the region between the graph of f and the x-axis on the interval 0 < x < 1. Find the volume V of the solid of revolution generated by revolving R about the x-axis.
I’ve been trying all night to figure this problem out with no luck at all. Please help!
Use the method of disks.
Draw the region R and a typical disk. This disk has a radius of [e^(-3x/2) - 0] and a thickness of dx. It contribues an increment of volume dV given by
dV = πr²dx = π(e^(-3x/2))² dx
= π e^(-3x) dx
The total volume V is given by
1
∫ π e^(-3x) dx
0
Use the method of disks.
Draw the region R and a typical disk. This disk has a radius of [e^(-3x/2) - 0] and a thickness of dx. It contribues an increment of volume dV given by
dV = πr²dx = π(e^(-3x/2))² dx
= π e^(-3x) dx
The total volume V is given by
1
∫ π e^(-3x) dx
0
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