MAC 2313 Midterm: MAC2313 F13 Test 3
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Some answers will involve fractions, , etc (1) (20 pts. ) Let d denote the solid region inside both the ellipsoid 4x2 + 4y2 + z2 = 64 and the cylinder x2 + y2 = 4. Zzzd (x2 + y2)dv as an iterated integral in (a) rectangular coodinates. (b) cylindrical coordinates. Let r be the triangular region in the (x, y)-plane with vertices (0, 0), ( 1, 0), and (0, 2). Let s denote the part of the paraboloid z = a2. Y2 that lies above the circle y2 = x(a x), where a > 0 is a constant. Let d denote the solid region under s and above the (x, y)-plane. (a) write iterated integrals in rectangular coordinates for: X2 (i) the volume of d. (ii) the surface area of s. Do not evaluate. (b) write both of the integrals of part (a) as iterated integrals in cylindrical coordinates.
