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Warning: The hard deadline has passed. You can attempt it, but you will not get credit for it. You are welcome to try it as a learning exercise.

Quiz 4: There is one question for each of the 8 topics from week 4. The time limit is 1 hour and you only get one try so make sure you have your notes and the week 4 slides handy. Good luck!

Question 1

Compute the iterated integral ∫30∫21x2ydydx. (provide a numeric answer out to the tenth)
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Question 2

For practice work the following equations:

Let D={(x,y):x2+y2≤1,y≥0}. What iterated integral would you use to compute ∬Df(x,y)dA?

Question 3

Suppose we want to use the change of variables s=xy and t=yx (for x>0, y>0) to compute the double integral ∬Df(x,y)dxdy. What is the Jacobian of the change of variables?
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Question 4

Consider the double integral ∬Df(x,y)dxdy. What is the Jacobian of the change of variables x=u2−v2, y=2uv?
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Question 5

Use the fact that the integrand is separable to compute ∫30∫21x2ydxdy. (provide a numeric answer out to the tenth)
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Question 6

For practice work the following equations:

Rewrite the integral ∫1−1∫1−x2√0(x2+y2)dydx in polar coordinates.

Question 7

For practice work the following equations:

Rewrite the integral ∫10∫1−x2√0e(x2+y2)dxdy in polar coordinates.

Question 8

Compute ∫∞−∞2π−−√exp[−(t−4)218]dt. (please provide answer as a numerical response.)
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