Which of the following statements are true? I. Let R be the region bounded by r +y = 1, a + y = 3, y? – r² = 1 and r - y² = 1. Then dA = ueu" du dv for R the substitution u = x- y and v =r+y. II. The volume of the region S that is inside the cylinder r? +y = a, above the plane z = 0 and below the plane z = 4- y is 4na. 2-z -2-2-y III. The integral I represents the volume of the tetrahedral region bounded by planes z = dz dy dr 0, y = 0, z = 0 and r + y+z = 2. -2 IV. The integral calculates the volume of the region above the plane z = 0, inside the sphere a +y? + 2? = 4 and outside the sphere a? +y? + (z - 1)? = 1. do (a) I only (b) III only (c) I, III (d) II, III (e) I, IV
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Calculus II
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