Question

In 1TF and 2TF set up the definite integral of the volume of the solid. Both the volume should be the same. Verify that this is the case for the previous two-volume calculations.

Short answer

Both volumes are the same.

Step-by-step solution

Given Information

The two integrals which show the volume of a solid,

$I_1=\pi {\int }_1^3(\ln x{)}^{3}dx$

$I_2=2\pi {\int }_0^{\ln 3}y(3-e^y)dy$

Calculate the integration

$I_1=\pi {\int }_1^3(\ln x{)}^{3}dx$

Using a calculator the value is $I_1=3.23$.

$I_2=2\pi {\int }_0^{\ln 3}y(3-e^y)dy$

Using a calculator the value is $I_2=3.23$.

Hence verified.