MATH 221 – Exercises on Area

For each of the following find the area of the given region R. Include all integrals that are needed.

1. R is bounded by the x-axis, the lines x = 0, x = 3, and the graph of f(x) = 3x³ + 2.

2. R is bounded by the x-axis, the lines x = 0, x = 3, and the graph of f(x) = x² – 4.

3. R is bounded by the graphs of and

4. R is bounded by the graphs of f(x) = 2x + 1 and g(x) = x³ – 2x +1.

5. R is bounded by f(x) = 2x + 1, g(x) = 9 – x², x = -1, and x = 3.

6. R is the region in the first quadrant bounded by the y-axis, f(x) = sin(x), and g(x) = cos(x).