Exercises

Exercises for Lecture #6

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1. Evaluate each of the following iterated integrals.

(a) (b)

(c) (d)

2. Evaluate the following definite integrals over the given rectangles.

(a) , D = [0; 2] x [0; 1] (b) , D = [1; 2] x [1; 3]

(c) , D = [0; 1] x[0; 2] (d) , D = [1; 2] x [0; 1]

3. For each of the following, evaluate the iterated integrals and sketch the region of integration.

(a) (b)

(c) (d)

4. Find the volume of the region beneath the graph of

a) and above the rectangle D = [-1; 1] x[-2; 2].

b) and above the region . Sketch the region D.

5. Evaluate , where D is the region bounded by the x-axis, the y-axis, and the line

6. Evaluate , where .

7. Find the volume of the region in described by .

8. Find the volume of the region in lying above the xy-plane and below the surface with equation .

9. Find the volume of the region in lying above the xy-plane and below the surface with equation

10. Evaluate each of the following iterated integrals.

(a) (b)

11-20. Calculate the double integrals:

11. 1. 2.

12. 1. 2.

13. 1. 2.

14. 1. 2.

15. 1. 2.

16. 1. 2.

17. 1. 2.

18. 1. 2.

19. 1. 2.

20. 1. 2.