Let R be the region in the first quadrant bounded by the line y = 5 and the graphs and y = 5 – x2. Write an integral expression for the area of R, using horizontal slices.
The region R looks like this:
This problem is very similar to the previous one, except that now the horizontal slice stretches from the graph of y = 5 – x2 on the left to the graph of on the right:
The width of the slice at height y is now , so the area of that slice is
The variable y ranges from 1 to 5, so the area of R is