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