Question 1

Evaluate the integral by reversing the order of integration.

Accepted Answer

The answer of Evaluate the integral by reversing the order...

Question 2

Evaluate the double integral  ,where  is the region bounded by the graphs of  and  .

Accepted Answer

The answer of Evaluate the double integral  ,where ...

Question 3

Calculate the iterated integral.

Accepted Answer

The answer of Calculate the iterated integral. ...

Question 4

Evaluate the double integral.   is bounded by  and  .

Accepted Answer

The answer of Evaluate the double integral.   is...

Question 5

The double integral  ,where  ,gives the volume of a solid.Describe the solid.

Accepted Answer

The answer of The double integral  ,where  ,gives...

Question 6

Evaluate the double integral.   is bounded by the circle with center the origin and radius 36.

Accepted Answer

The answer of Evaluate the double integral.   is...

Question 7

Calculate the double integral.Round your answer to two decimal places.

Accepted Answer

The answer of Calculate the double integral.Round your answer to...

Question 8

Evaluate the iterated integral  by reversing the order of integration.

Accepted Answer

The answer of Evaluate the iterated integral  by reversing...

Question 9

Evaluate the integral by reversing the order of integration.

Accepted Answer

The answer of Evaluate the integral by reversing the order...

Question 10

Estimate the volume of the solid that lies above the square  and below the elliptic paraboloid  . Divide  into four equal squares and use the Midpoint rule.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Estimate the volume of the solid that...

Question 11

Evaluate  where D is the figure bounded by  and  .

Accepted Answer

The answer of Evaluate  where D is the figure...

Question 12

Calculate the double integral.Round your answer to two decimal places.

Accepted Answer

The answer of Calculate the double integral.Round your answer to...

Question 13

Evaluate the double integral by first identifying it as the volume of a solid. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The integral given is
$$\int_{-1}^1\int_0^{4-x^2}3z^2\,dz\,dA$$
which is the volume of the solid that lies under the graph $z=3y^2$, above the region $D$ in the $xy$-plane where $D$ is the disk of radius 1 centered at the origin. Thus, the volume is a portion of a paraboloid of revolution cut off by a plane, and the integral can be evaluated as
$$\int_{-1}^1\int_0^{4-x^2}3z^2\,dz\,dA = \int_{-1}^1\int_0^{\sqrt{4-x^2}}3(3y^2)^2\,dy\,dx = \int_{-1}^1\frac{27}{5}(4-x^2)^{\frac{5}{2}}\,dx = \frac{256}{5\sqrt{5}}.$$

Question 14

Evaluate the double integral.  ,  is triangular region with vertices  .

Accepted Answer

The answer of Evaluate the double integral.  , ...

Quiz 12: Multiple Integrals

Evaluate the integral by reversing the order of integration.

Evaluate the double integral ,where is the region bounded by the graphs of and .

Calculate the iterated integral.

Evaluate the double integral. is bounded by and .

The double integral ,where ,gives the volume of a solid.Describe the solid.

Evaluate the double integral. is bounded by the circle with center the origin and radius 36.

Calculate the double integral.Round your answer to two decimal places.

Evaluate the iterated integral by reversing the order of integration.

Evaluate the integral by reversing the order of integration.

Estimate the volume of the solid that lies above the square and below the elliptic paraboloid . Divide into four equal squares and use the Midpoint rule.

Evaluate where D is the figure bounded by and .

Calculate the double integral.Round your answer to two decimal places.

Evaluate the double integral by first identifying it as the volume of a solid.

Evaluate the double integral. , is triangular region with vertices .