A(x)=(10e^.01x)^2 for 0<=x<=10,find the volume.

Question

find the volume of the solid with cross-sectional area A(x):

A(x)=10e^.01x, 0<=x<=10

Answer 1

A(x)=(100e^0.01x)² is the cross-section area, so A(x)=10000e^0.02x. Volume of a thin disc with this cross-section area is 10000e^0.02x​dx, where dx is the infinitesimal thickness of the disc. So V=∫A(x)dx=10000∫₀¹⁰e^0.02xdx=10000[e^0.02x/0.02]₀¹⁰.

V=500000(e^0.2-1)=500000(1.2214-1)=110,700 cubic units approximately.