Integration for Volume Given Cross Sections

1. The problem statement, all variables and given/known data

The roof and walls of a storage building are built in the shape modeled by the curve y(x) = 20 - [tex]\frac{x^6}{3,200,000}[/tex]. Each cross section cut perpendicular to the x-axis is a rectangle with a base of 50 feet and a height of y feet.

In cubic feet the volume of the building is approximately:

A) 686
B) 2,000
C) 17,100
D) 34,300
E) 50,000

2. Relevant equations

Area = (50)(y(x)) = 50 ( 20 - [tex]\frac{x^6}{3,200,000}[/tex] )

3. The attempt at a solution

Given the equation above, I reasoned that the area is the base (the 50 feet) multiplied by the function y(x). I carried the following integration:

V = [tex]\int^{0}_{20}[/tex] 50 * ( 20 - [tex]\frac{x^6}{3,200,000}[/tex] )

I get an answer of 17142.86. Is this correct? It's a little off from the problem.

 

Thank you!