QUESTION

# 1) Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you...

1) Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer.

Enclosed by y = −x and y = −x3

2) Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer. HINT [See Example 3.]

Enclosed by y = x and y = x4

3) Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer. (Round your answer to four significant digits.)

Enclosed by y = ex, y = 2x + 1, x = −3, and x = 1

4) Suppose your annual income is

I(t) = 49,000 + 2,000t (0 ≤ t ≤ 3)

dollars per year, where t represents the number of years since you began your job, while your annual expenses are

E(t) = 38,000 + 1,500t (0 ≤ t ≤ 3)

dollars per year. Find the area between the graphs of I(t) and E(t)for 0 ≤ t ≤ 3.

5) Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer. HINT [See Example 2.]

Between y = −x and y = −x3 for x in [−1, 1]

6) Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer.

Between y = −x and y = x for x in [0, 2]

7) Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer. HINT [See Example 1.]

Between y = x2 and y = −1 for x in [−1, 1]