From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!

# Assumptions When Finding Area Exercises

### Example 1

Let R be the region above the line  and below the graph of y = cos x on the interval

Write an integral expression for the area of R,

(a) vertical slices

(b) horizontal slices

### Example 2

Let R be the region bounded by the curve y = x4 and the lines x = 2 and y = 81. Write an integral expression for the area of R, using

(a) vertical slices

(b) horizontal slices

### Example 3

Let R be the region in the first quadrant bounded by the graph of x2 + y2 = 1 and the x- and y- axes. Write an integral expression for the area of R, using

(a) vertical slices

(b) horizontal slices

### Example 4

Let R be the region bounded by the graphs of y = ex, y = 1, and x = 3.

Write an integral expression for the area of R, using

(a) vertical slices

(b) horizontal slices

### Example 5

Let R be the region above the graph of y = 1 – x2 and below the graph x2 + y2 = 1. Write an integral expression for the area of R, using vertical slices.

### Example 6

Let R be the region in the first quadrant bounded by the x-axis and the graphs  and y = 5 – x2. Write an integral expression for the area of R, using horizontal slices.

### Example 7

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.

### Example 8

Let R be the region between the graphs , y = x2, and the line x = 4.

Write an integral expression for the area of R, using vertical slices.

### Example 9

Let R be the region in the first quadrant bounded by the x-axis and the graphs  and y = 5 – x2. Write an integral expression for the area of R, using vertical slices.

### Example 10

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 vertical slices.

### Example 11

Let R be the region between the graphs of y = x4 + 1 and y = x2 + 1 for 1 ≤ y ≤ 5. Write an integral expression for the area of R, using

(a) vertical slices

(b) horizontal slices

### Example 12

Let R be the region shown below.

Write an integral expression for the area of R, using vertical slices.