Volume from cross-sectional area: integrating 4x² from 0 to 5

[ver_mathstats]

Homework Statement

The base of the solid is a square, one of whose sides is the interval [0,5] along the the x-axis.
The cross sections perpendicular to the x-axis are rectangles of height f(x)=4x^2. Compute the volume of the solid.

Relevant Equations

f(x)=4x^2

I know that the formula for volume is equal to the definite integral ∫A(x)dx, where A(x) is the cross sectional. I found the definite integral where b=5 and a=0, for ∫4x²dx. I obtained the answer 500/3, however this was incorrect, and I'm unsure of where I went wrong?

Thank you.

 

[Orodruin]

You have not integrated the area, you have integrated the height.