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⁻⁵ˣ, y = 0, x = 0, x = 6

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. First, we express the equation y = e⁻⁵ˣ as x = ln(y). The bounds for the region are x = 0 and x = 6. Now, we set up the integral for the volume:
ntegrate from x = 0 to x = 6

Multiply the integrand by 2πx to get the circumference of the cylinder at each x-value

Integrate the result and evaluate the definite integral
The volume of the solid generated is approximately 38.635 cubic units.