Calculus homework

Question 1

1.

Find the average value of the function f over the given region.

f(x, y) = ; R = {(x, y): 1 ≤ x ≤ 4, 1 ≤ y ≤ 4}

2

2

5 points

Question 2

1.

Evaluate the double integral over the given region.

R = {(x, y): 0 ≤ x ≤ 1, 0 ≤ y ≤ 3}

4 ln 2

ln 2

ln 2 ln 4

ln 8

5 points

Question 3

1.

Evaluate the integral.

-

- 70

- 10

-

5 points

Question 4

1.

Evaluate the integral.

17

476

119

68

5 points

Question 5

1.

Evaluate the double integral over the given region.

R = {(x, y): 0 ≤ x ≤ π, 0 ≤ y ≤ 1}

8π - 8

π

8π

5 points

Question 6

1.

Evaluate the integral.

-

-

5 points

Question 7

1.

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral.

The lines , , and

5 points

Question 8

1.

Evaluate the double integral over the given region.

R = {(x, y): 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}

5 points

Question 9

1.

Find the average value of the function f over the given region.

f(x, y) = e2x; R =

e - 1

2e - 1

5 points

Question 10

1.

Evaluate the integral.

25

15

13

-45

5 points

Question 11

1.

Evaluate the integral.

10π

11π

21π

20π

5 points

Question 12

1.

Evaluate the double integral over the given region.

R = {(x, y): 0 ≤ x ≤ 1, 0 ≤ y ≤ 2}

-

5 points

Question 13

1.

Find the average value of the function f over the given region.

f(x, y) = ; R = {(x, y): 1 ≤ x ≤ 10, 1 ≤ y ≤ 10}

5 points

Question 14

1.

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral. The curves and

5 points

Question 15

1.

Evaluate the integral.

40

20

160

320

5 points

Question 16

1.

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral.

The lines , , and

5 points

Question 17

1.

Find the average value of the function f over the given region.

f(x, y) = over the region bounded by , , , and .

ln 2

6 ln 2

ln 2

ln 2

5 points

Question 18

1.

Find the average value of the function f over the given region. f(x, y) = ex2 over the region bounded by , , , and .

2e - 1

e - 1

5 points

Question 19

1.

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral.

The parabola and the line

5 points

Question 20

1.

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral.

The curve and the lines and

5 points