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20Chw7

# 20Chw7 - MATH 20C graded homework 7(20 points 15.3#16(10...

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Unformatted text preview: MATH 20C graded homework 7. (20 points) 15.3 #16 (10 points): Integrate f ( x,y,z ) = z over the region W below the upper hemisphere of radius 3 , but lying over the triangle in the xy-plane bounded by the lines x = 1 , y = 0 , and x = y . Solution: The region W is z-simple; it projects onto the region D (which may be taken as vertically or horizontally simple; both iterations are provided below). The sphere of radius 3 has equation x 2 + y 2 + z 2 = 9, and the top half has equation z = p 9- x 2- y 2 . Thus, each vertical line segment in W runs from ≤ z ≤ p 9- x 2- y 2 . The base D looks like .............................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
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20Chw7 - MATH 20C graded homework 7(20 points 15.3#16(10...

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