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Set Up an Iterated Integral For Wf(x,y,z)dV\int _ { W } f ( x , y , z ) d V

Question 21

Multiple Choice

Set up an iterated integral for Wf(x,y,z) dV\int _ { W } f ( x , y , z ) d V , where W is the solid region bounded below by the rectangle 0 \le x \le 3, 0 \le y \le 1 and above by the surface z2+y2=1z ^ { 2 } + y ^ { 2 } = 1


A) Wf(x,y,z) dV=030101y2f(x,y,z) dzcxαdy\int _ { W } f ( x , y , z ) d V = \int _ { 0 } ^ { 3 } \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { \sqrt { 1 - y ^ { 2 } } } f ( x , y , z ) d z c x \alpha d y
B) Wf(x,y,z) dV=030101y2f(x,y,z) dydzdx\int _ { W } f ( x , y , z ) d V = \int _ { 0 } ^ { 3 } \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { \sqrt { 1 - y ^ { 2 } } } f ( x , y , z ) d y d z d x
C) Wf(x,y,z) dV=030101y2f(x,y,z) dzdydx\int _ { W } f ( x , y , z ) d V = \int _ { 0 } ^ { 3 } \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { \sqrt { 1 - y ^ { 2 } } } f ( x , y , z ) d z d y d x
D) Wf(x,y,z) dV=03011y21y2f(x,y,z) dzdydx\int _ { W } f ( x , y , z ) d V = \int _ { 0 } ^ { 3 } \int _ { 0 } ^ { 1 } \int _ { - \sqrt { 1 - y ^ { 2 } } } ^ { \sqrt { 1 - y ^ { 2 } } } f ( x , y , z ) d z d y d x
E) Wf(x,y,z) dV=03011y21y2f(x,y,z) dydxdz\int _ { W } f ( x , y , z ) d V = \int _ { 0 } ^ { 3 } \int _ { 0 } ^ { 1 } \int _ { - \sqrt { 1 - y ^ { 2 } } } ^ { \sqrt { 1 - y ^ { 2 } } } f ( x , y , z ) d y d x d z

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