Exam 3 Solution on Calculus III

# Exam 3 Solution on Calculus III - Name OgreOgre...

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Name: OgreOgre TEST3/MAC2313 Page 1 of 6 _________________________________________________________________ Read Me First: Show all essential work very neatly. Use correct notation when presenting your computations. Write using complete sentences. Remember this: "=" denotes "equals" , " " denotes "implies" , and " " denotes "is equivalent to". Generic vector objects must be denoted by using arrows. Since the answer really consists of all the magic transformations, do not "box" your final results. Show me all the magic on the page neatly. _________________________________________________________________ 1. (10 pts.) Convert the given iterated integral into an iterated integral in polar coordinates that has the same numerical value and is easier to evaluate, perhaps. Do not attempt to evaluate the polar integral. A picture might help. 0 4 0 (16 x 2 ) 1/2 e ( x 2 y 2 ) dydx 3 π /2 π 4 0 re r 2 drd θ . _________________________________________________________________ 2. (10 pts.) Write down, but do not attempt to evaluate the triple iterated integral in spherical coordinates that provides the volume of the solid T that is bounded above by the sphere defined by x

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