PHYS 201 Midterm: PHYS 201 Drexel Exam2 Solutions
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Score: (10 points) sketch the region whose area is given by the integral and evaluate the integral: 1: (10 points) evaluate the triple integralrrre dv where e is bounded by planes x = 0, y = 0, z = 0 and 2x + 2y + z = 4. Solution: notice that the plane 2x+2y+z = 4 intersects the xy-plane at 2x+2y = 4. Consider e to be a type i 3-d region, then we have. E = {(x, y, z) | (x, y) d, 0 z 4 2x 2y}, where d is the triangle. D = {(x, y) | 0 x 2, 0 y 2 x}. Z 4 2x 2y (4 2x 2y) dy dx. =z 2 ((4 2x)y y2)|y=2 x (2 x)3|x=2 x=0 = 2: (10 points) find the area of the part of surface z = xy that lies in the cylinder x2 + y2 = 4.
