Question

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis.

y=e−⁷ˣ
y=0
x=0
x=2
​

Answer 1

To find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis, we can use the method of cylindrical shells.

Step-by-step explanation:

To find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis, we can use the method of cylindrical shells.

The volume can be calculated by integrating the area of a single shell over the range of x-values. With the given equations y = e^(-7x), y = 0, x = 0, and x = 2, we can set up the integral as follows:

V = 2π∫(x)(e^(-7x))dx, where the limits of integration are from 0 to 2. Evaluating this integral will give us the volume of the solid.