Calculus Help

Name: Worksheet: Area Under a Curve - Part I Section:

1. Determine the exact area between the graph of the function and the x-axis for each given interval.

(a) x�[0, 4]

−4 −2 2 4

−4

−2

2

4

(b) x�[0, 6]

−4 −2 2 4

−4

−2

2

4

(c) x�[−2, 3]

−4 −2 2 4

−4

−2

2

4

2. Determine the left-hand sum and right-hand sum for the following curve over the domain x�[0, 8] when n = 4.

4 8

4

8

12

16

20

For use with OpenStax Calculus, free at https://openstax.org/details/books/calculus-volume-1 1

Name: Worksheet: Area Under a Curve - Part I Section:

3. Determine the left-hand sum and right-hand sum for the following curve over the domain x�[−2, 3] when n = 5.

−2 2 4

4

8

12

16

20

24

28

4. Determine the left-hand sum and right-hand sum for the following curve over the domain x�[0, 1] when n = 4.

−2 −1 1 2 −2

2

4

6

8

10

12

14

5. Determine the left-hand sum for the function f (x) = x3 − 4x + 1 over the interval x�[0, 2] when n = 8. Use a graphing utility to help you visualize the sum.

For use with OpenStax Calculus, free at https://openstax.org/details/books/calculus-volume-1 2