Thread: volume of solid of revolution

1. volume of solid of revolution

consider $\displaystyle B>1.$

compute the volume of revolution given the curve $\displaystyle y=\sqrt xe^{-x^2}$ between $\displaystyle y=\sqrt Be^{-B^2}$ and $\displaystyle y=e^{-1}$ revolving the $\displaystyle x$ axis.

don't know how to set up the integral.

thanks for the help.

2. Originally Posted by palpyko
consider $\displaystyle B>1.$

compute the volume of revolution given the curve $\displaystyle y=\sqrt xe^{-x^2}$ between $\displaystyle y=\sqrt Be^{-B^2}$ and $\displaystyle y=e^{-1}$ revolving the $\displaystyle x$ axis.

don't know how to set up the integral.

thanks for the help.
The volume of a solid which is produced by revolution of the curve y = f(x) about the x-axis is calculated by

$\displaystyle V = \pi \int y^2 dx$

From $\displaystyle y=e^{-1}$ you know that x = 1 and

from $\displaystyle y=\sqrt Be^{-B^2}$ you know that x = B > 1

Use the formula given above to calculate the volume. Use integration by substitution.