Question 1

Evaluate $\iint _ { R } \sqrt { 4 - x ^ { 2 } } d A$ where $R = [ - 2,2 ] \times [ 0,3 ]$ by first identifying it as the volume of a solid.

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Question 2

Compute the Riemann sum for the double integral $\iint _ { R } x + 2 y d A$ where $R = [ 0,6 ] \times [ 0,2 ]$ for the given grid and choice of sample points.

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Question 3

Compute the Riemann sum for the double integral $\iint _ { R } x + 2 y d A$ where $$R = [ 0,6 ] \times [ 0,2 ]$$ for the given grid and choice of sample points.

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Question 4

Evaluate $\iint _ { R } \sqrt { 9 - y ^ { 2 } } d A$ where $R = [ - 2,2 ] \times [ 0,3 ]$ by first identifying it as the volume of a solid.

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Question 5

Use the Midpoint Rule to estimate $\iint _ { R } ( 7 - 2 x - y ) d A$ over $R = \{ ( x , y ) \mid - 1 \leq x \leq 2 , - 1 \leq y \leq 2 \}$ partitioned by the lines x = 0, x = 1, y = 0, and y = 1 into nine subrectangles.

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Question 6

Evaluate $\iint _ { R } 3 d A$ where $R = [ - 1,1 ] \times [ 2,3 ]$ by first identifying it as the volume of a solid.

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Question 7

Compute the Riemann sum for the double integral $\iint _ { R } x + 2 y d A$ where $R = [ 0,6 ] \times [ 0,2 ]$ for the given grid and choice of sample points.

Accepted Answer

The answer of Compute the Riemann sum for the double...

Question 8

Compute the Riemann sum for the double integral $\iint _ { R } x + 2 y d A$ where $R = [ 0,6 ] \times [ 0,2 ]$ for the given grid and choice of sample points.

Accepted Answer

The answer of Compute the Riemann sum for the double...

Question 9

Give an example of a non-constant function f(x, y) such that the average value of f over $R = \{ ( x , y ) \mid - 1 \leq x \leq 1 , - 1 \leq y \leq 1 \}$ is 0.

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Question 10

Compute the Riemann sum for the double integral $\iint _ { R } 4 d A$ where $R = [ 0,6 ] \times [ 0,2 ]$ for the given grid and choice of sample points.

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Quiz 12: Multiple Integrals

Evaluate ∬R4−x2dA\iint _ { R } \sqrt { 4 - x ^ { 2 } } d A∬R​4−x2​dA where R=[−2,2]×[0,3]R = [ - 2,2 ] \times [ 0,3 ]R=[−2,2]×[0,3] by first identifying it as the volume of a solid.

Compute the Riemann sum for the double integral ∬Rx+2ydA\iint _ { R } x + 2 y d A∬R​x+2ydA where R=[0,6]×[0,2]R = [ 0,6 ] \times [ 0,2 ]R=[0,6]×[0,2] for the given grid and choice of sample points.

Compute the Riemann sum for the double integral ∬Rx+2ydA\iint _ { R } x + 2 y d A∬R​x+2ydA where R=[0,6]×[0,2]R = [ 0,6 ] \times [ 0,2 ]R=[0,6]×[0,2] for the given grid and choice of sample points.

Evaluate ∬R9−y2dA\iint _ { R } \sqrt { 9 - y ^ { 2 } } d A∬R​9−y2​dA where R=[−2,2]×[0,3]R = [ - 2,2 ] \times [ 0,3 ]R=[−2,2]×[0,3] by first identifying it as the volume of a solid.

Evaluate ∬R3dA\iint _ { R } 3 d A∬R​3dA where R=[−1,1]×[2,3]R = [ - 1,1 ] \times [ 2,3 ]R=[−1,1]×[2,3] by first identifying it as the volume of a solid.

Compute the Riemann sum for the double integral ∬Rx+2ydA\iint _ { R } x + 2 y d A∬R​x+2ydA where R=[0,6]×[0,2]R = [ 0,6 ] \times [ 0,2 ]R=[0,6]×[0,2] for the given grid and choice of sample points.

Compute the Riemann sum for the double integral ∬Rx+2ydA\iint _ { R } x + 2 y d A∬R​x+2ydA where R=[0,6]×[0,2]R = [ 0,6 ] \times [ 0,2 ]R=[0,6]×[0,2] for the given grid and choice of sample points.

Give an example of a non-constant function f(x, y) such that the average value of f over R={(x,y)∣−1≤x≤1,−1≤y≤1}R = \{ ( x , y ) \mid - 1 \leq x \leq 1 , - 1 \leq y \leq 1 \}R={(x,y)∣−1≤x≤1,−1≤y≤1} is 0.

Compute the Riemann sum for the double integral ∬R4dA\iint _ { R } 4 d A∬R​4dA where R=[0,6]×[0,2]R = [ 0,6 ] \times [ 0,2 ]R=[0,6]×[0,2] for the given grid and choice of sample points.

Evaluate $\iint _ { R } \sqrt { 4 - x ^ { 2 } } d A$ where $R = [ - 2,2 ] \times [ 0,3 ]$ by first identifying it as the volume of a solid.

Evaluate $\iint _ { R } \sqrt { 9 - y ^ { 2 } } d A$ where $R = [ - 2,2 ] \times [ 0,3 ]$ by first identifying it as the volume of a solid.

Evaluate $\iint _ { R } 3 d A$ where $R = [ - 1,1 ] \times [ 2,3 ]$ by first identifying it as the volume of a solid.

Give an example of a non-constant function f(x, y) such that the average value of f over $R = \{ ( x , y ) \mid - 1 \leq x \leq 1 , - 1 \leq y \leq 1 \}$ is 0.