Question

Write a Riemann sum and then a definite integral representing the volume of the region, using the slice shown in the figure below. Evaluate the integral exactly. Use your work to answer the questions below.

http://www.webassign.net/userimages/8.1.012.jpg?db=v4net&id=53286

What is the approximate volume of the slice with respect to y?

Answer 1

The half-circle has equation x²+y²=49.
At height y, this means that x = sqrt(49-y²)
So the approximate volume of this slice is 2*√(49-y²)*10*Δy

Now try to make the Riemann-sum and convert to an integral...

Answer 2

thank you. integral 0 to 7 [2*√(49-y²)*10*dy]