MAT 267- Exam 3 Practice Questions with answers

MAT 267- Exam 3 Practice Questions with answers - MAT 267...

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MAT 267 Spring 2015 Jeremiah Jones Test 3 Solutions Multiple Choice 1) Evaluate E ze 2 x + y where E is the box 0 x 2, 0 y 3, 0 z 5. The iterated integral is written as 2 0 3 0 5 0 ze 2 x + y dz dy dx. Since ze 2 x + y = ze 2 x e y , the integrand is separable and we can do each of the single integrals sepa- rately: 2 0 3 0 5 0 ze 2 x + y dz dy dx = 2 0 e 2 x dx 3 0 e y dy 5 0 z dz. The x integral is 2 0 e 2 x dx = 1 2 e 2 x x =2 x =0 = 1 2 ( e 4 - 1) . The y integral is 3 0 e y dx = e y y =3 y =0 = ( e 3 - 1) . The z integral is 5 0 z dz = 1 2 z 2 z =5 z =0 = 25 2 . The triple integral is the product of these three numbers: 2 0 3 0 5 0 ze 2 x + y dz dy dx = 25 4 ( e 4 - 1)( e 3 - 1) 6393 . 43 . 2) Let E be the solid region bounded by sphere of radius 4 in the first octant. Find the appropriate integral for E x 2 + y 2 + z 2 dV in spherical coordinates. The first octant corresponds to 0 φ π/ 2 and 0 θ π/ 2. The integrand is just x 2 + y 2 + z 2 = ρ and the differential volume dV in spherical coordinates is dV = ρ 2 sin( φ ) . The triple integral in spherical coordinates is thus π/ 2 0 π/ 2 0 4 0 ρ ρ 2 sin( φ ) dρ dφ dθ = π/ 2 0 π/ 2 0 4 0 ρ 3 sin( φ ) dρ dφ dθ.
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  • Spring '14
  • England
  • Calculus, Multiple integral, dz dy dx, Jeremiah Jones, ze2x+y dz dy

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