calc_tutorial_15_4_017

 
Problem Statement

{2,4,6,8}
round(2/8,2)
round(4*0.25,2)

Calculate the integral over the given region by changing to polar coordinates.

f(x, y) = |2xy|; x2 + y2 ≤ 1

 
Step 1

Question Sequence

Question 1

Express region D = {(x, y) | x2 + y2 ≤ 1} in polar coordinates.

0 ≤ r ≤

0 ≤ θ ≤ π

Correct.
Incorrect.

 
Step 2

Question Sequence

Question 2

Express the double integral in polar coordinates.

A.
B.
C.
D.
Correct.
Incorrect.

 
Step 3

Question Sequence

Question 3

Evaluate the inner integral and use the trigonometric identity sin 2θ = 2 cos θ sin θ. Round your answer to two decimal places.

=

Correct.
Incorrect.

 
Step 4

Question Sequence

Question 4

In order to evaluate , we must find where sin 2θ is positive and negative in the interval [0, 2π].

By graphing sin 2θ, state the values θ where |sin 2θ| = sin 2θ. That is, find where sin 2θ is positive.

0 ≤ θ ≤

A.
B.

and

π ≤ θ ≤

A.
B.

State the values θ where |sin 2θ| = −sin 2θ. That is, find where sin 2θ is negative.

A.
B.

≤ θ ≤ π

and

A.
B.

≤ θ ≤ 2π

Correct.
Incorrect.

 
Step 5

Question Sequence

Question 5

Using the intervals found above, express as a sum/difference of positive integrals.

=

Correct.
Incorrect.

 
Step 6

Question Sequence

Question 6

Evaluate .

=

Correct.
Incorrect.

 
Step 7

Question Sequence

Question 7

Evaluate using polar coordinates. Round your answer to two decimal places.

=

Correct.
Incorrect.