Question

The base of a solid is the region in the first quadrant bounded by the graph of y = 3/(e^x) , the x-axis, the y-axis, and the line x=2. Each cross section of this solid perpendicular to the x-axis is a square. What is the volume of the solid?

Answer 1

Each square cross-section has width y and height y, so its area is y^2 = 9e^(-2x)

So, the volume is the sum of all those squares, or

∫[0,2] 9e^(-2x) dx