Question

Find the volume V of the solid obtained by rotating the region bounded by the curves y = 5e⁽⁻ˣ⁾, y = 5, x = 6 about the line y = 10.

Answer 1

To find the volume of the solid, use the method of cylindrical shells and set up the integral V = 2π ∫(10 - 5e⁽⁻ˣ⁾)x dx.

Step-by-step explanation:

To find the volume of the solid obtained by rotating the region bounded by the curves y = 5e⁽⁻ˣ⁾, y = 5, and x = 6 about the line y = 10, we can use the method of cylindrical shells.

First, we need to determine the limits of integration by finding the x-coordinate of the point where the curves intersect, which is x = ln(5).

Then, we can set up the integral: V = 2π ∫[ln(5), 6] (10 - 5e⁽⁻ˣ⁾)x dx. Evaluating this integral will give us the volume of the solid.