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Find the volume under the surface z = f(x,y) and above the rectangle with the given boundaries. 30) z = 6x^2y

Question : Find the volume under the surface z = f(x,y) and above the rectangle with the given boundaries. 30) z = 6x^2y : 2151842

Find the volume under the surface z = f(x,y) and above the rectangle with the given boundaries.

30) z = 6x2y; 0 ≤ x ≤ 4, 0 ≤ y ≤ 3

A) 1256

B) 676

C) 2256

D) 576

31) z = x2 + y2; 0 ≤ x ≤ 1, 0 ≤ y ≤ 1

A) (4/3)

B) (1/3)

C) (2/3)

D) (8/3)

32) z = 8x + 4y + 7; 0 ≤ x ≤ 1, 1 ≤ y ≤ 3

A) 38

B) 36

C) 28

D) 26

33) z = x3; 0 ≤ x ≤ 2, 0 ≤ y ≤ 3

A) 18

B) 6

C) 12

D) 4

34) z = (8/(x + y)3); 0 ≤ x ≤ 1, 1 ≤ y ≤ 2

A) (4/3)

B) (1/3)

C) (8/3)

D) (2/3)

35) z = (x + y)2; -1 ≤ x ≤ 1, -1 ≤ y ≤ 1

A) (2/3)

B) (1/3)

C) (4/3)

D) (8/3)

36) z = (x/y); 0 ≤ x ≤ 1, 1 ≤ y ≤ e

A) (1/6)

B) (1/2)

C) (1/3)

D) (1/4)

37) z = e2x + 3y; 0 ≤ x ≤ 1, 0 ≤ y ≤ 1

A) (1/4)(e5 - e3 - e2 - 1)

B) (1/4)(e5 - e3 - e2 + 1)

C) (1/6)(e5 - e3 - e2 + 1)

D) (1/6)(e5 - e3 - e2 - 1)

38) z = 4x2 + 9y2; 0 ≤ x ≤ 1, 0 ≤ y ≤ 1

A) (26/3)

B) (13/3)

C) (17/3)

D) (5/3)

39) z = √(x) + √(y); 0 ≤ x ≤ 1, 0 ≤ y ≤ 1

A) (1/3)

B) (4/3)

C) (8/3)

D) (2/3)

Evaluate the double integral.

40)

A) 2

B) (8/3)

C) 4

D) (4/3)

41)

A) (25/2)

B) (9/2)

C) (25/4)

D) (9/4)

42)

A) 32

B) 16

C) 25

D) 50

43)

A) (2401/15)

B) (4802/15)

C) 686

D) 343

44)

A) (1/15)

B) (1/31)

C) (1/29)

D) (1/30)

45)

A) 54

B) 45

C) 63

D) 36

46)

A) (32/105)

B) (32/115)

C) (44/105)

D) (44/115)

47)

A) (7/24)

B) (25/24)

C) (9/24)

D) (5/24)

48)

A) (1/e)(e2 - e)2

B) (1/2)(e - 1)2

C) (1/2)(e2 - e)2

D) (1/3)(e - 1)2

Use the region R to evaluate the double integral.

49) ∫∫((2xy - y2 + 1)dydx))

R

R bounded by x = 2y + 2, x = 3 - 3y, y = 0

A) (33/250)

B) (125/33)

C) (33/50)

D) (31/14)

50) ∫∫(2xydxdy))

R

R bounded by y = x2 + 4, y = 3x + 2, x = -2, x = 1

A) (241/4)

B) (243/4)

C) - (241/4)

D) - (243/4)

51) ∫∫(dydx))

R

R bounded by y = √(x + 4), y = (3/5)x, y = 0

A) (27/2)

B) - (31/6)

C) - (27/2)

D) (31/6)

52) ∫∫(x2 + y2dxdy))

R

R bounded by x = 7, y = 0, and y = 3x

A) (40,817/4)

B) 7203

C) 1029

D) 147

53) ∫∫(x2 + y4dxdy))

R

R bounded by x = 0, y = 16, y = x2

A) (7,886,848/165)

B) (125,851,648/165)

C) (31,479,808/165)

D) (1,988,608/165)

54) ∫∫(exeydxdy))

R

R bounded by x = 0, x =lny, y =ln4

A) 8 - 4ln4 + e

B) 2ln4 - 6 + e

C) 6 - 2ln4 + e

D) 4ln4 - 8 + e

55) ∫∫((x3 - y3)dydx))

R

R bounded by x = 0, y = 1, y = x

A) - (3/20)

B) (1/3)

C) (1/6)

D) - (1/3)

56) ∫∫((x + y)dxdy))

R

R bounded by xy = 4, x + y = 5

A) 6

B) 12

C) 9

D) 8

57) ∫∫(x2y2dxdy))

R

R bounded by 0 ≤ x ≤ y, 1 ≤ y ≤ 3

A) (370/9)

B) (364/3)

C) (364/9)

D) (370/3)

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

58) f(x, y) = 4x + 5y; 0 ≤ x ≤ 1, 0 ≤ y ≤ 1

A) (9/2)

B) (13/2)

C) 9

D) 7

59) f(x, y) = 6x + 2y; 0 ≤ x ≤ 6, 0 ≤ y ≤ 4

A) 18

B) 22

C) 19

D) 20

60) f(x, y) = e4x; 0 ≤ x ≤ (1/4), 0 ≤ y ≤ (1/4)

A) (e - 1/4)

B) e - 1

C) (2e - 1/16)

D) 2e - 1

61) f(x, y) = (1/xy); 1 ≤ x ≤ 7, 1 ≤ y ≤ 7

A) (ln7/36)

B) (ln7/49)

C) ((ln7/6))2

D) ((ln7/7))2

62) f(x, y) = (1/(xy)2); 1 ≤ x ≤ 9, 1 ≤ y ≤ 9

A) (ln9/9)

B) (1/81)

C) (ln9/81)

D) (1/9)

Solution
5 (1 Ratings )

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