22.0k views
3 votes
Find the volume V of the solid obtained by rotating the region bounded by the curves y = 5e⁽⁻ˣ⁾, y = 5, x = 4 about the line y = 10.

User Dandaka
by
8.4k points

1 Answer

3 votes

Final answer:

To find the volume V of the solid obtained by rotating the region bounded by the curves y = 5e^-x, y = 5, x = 4 about the line y = 10, we can use the method of cylindrical shells.

Step-by-step explanation:

To find the volume V of the solid obtained by rotating the region bounded by the curves y = 5e-x, y = 5, x = 4 about the line y = 10, we can use the method of cylindrical shells.

First, we need to find the limits of integration, which are x = 0 and x = 4. Next, we find the height of each shell, which is the difference between the line y = 10 and the curve y = 5e-x. This gives us the height h = 10 - 5e-x.

The radius of each shell is the distance from the line y = 10 to the x-axis, which is 10 - y = 10 - 5e-x. Now, we can set up the integral:

V = 2π ∫[0,4] (10 - 5e-x)(10 - 5e-x) dx

Solving this integral will give us the volume of the solid.

User Tmtxt
by
8.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.