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MTH 234 Midterm: Test3Review
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turquoisegnu128
31 Jan 2019
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MSU
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Mathematics
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MTH 234
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All
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MTH 234 Midterm: Test4Review
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what is dydx for 51
J-IJ, Jo Jo 16-y 2xy dx dy42. 2x dx dy In2 c2 43. dx dy xy dx dy 45. 6 sin (2x 3y) dx dy 46. esiny dx dy dx 47-52. Evaluating integrals Evaluate the following integrals. A sketch is helpful. 47. 48. 49, sketch to n ãR12yd: RÃs bounded by y = 2-x, y = Vx, and y = 0. I Ry2 dA; Ris bounded by y=1,y=l-x, and y=x-1. 17x3xy dA: R is bounded by y=2-x, y=0, and x 4·-y2 in the first quadrant. d by 50. (x + y) dA: R is bounded by y = |x| and y = 4. 51. IfR3x2dA;Ris bounded by y=0,y=2x+ 4, and y=x3. 52. 17xx2 y d: R is bounded by y = 0, y = Vx, and y = x-2. 53-56. Volumes Use double integrals to calculate the volume of the following regions 53. The tetrahedron bounded by the coordinate planes the 54· The solid in the first octant bounded by the coordinate planes and 55. The segment of the cylinder x2y1 bounded above by the 56. The solid beneath the cylinder y and above the region (x = 0, y = 0, z 0) and the plane z = 8-2x-4y the surface z 1-y-x plane z = 12 + x + y and below by z 0 x + 5
What is double integral of dydx in 47 and 51
J-1J, Jo Jo 2xy dx dy42. 2x dx dy In2 2 43. dx dy xy dx dy Ï/2 Ï /2 45. 6 sin (2x 3y) dx dy 46. dx 47-52. Evaluating integrals Evaluate the following integrals. A sketch is helpful. 47. 48. 49, sketch to n ãR 12yd: RÃs bounded by y-2-x,y=Vx, and y=0. I Ry2 dA: Ris bounded by y=1.y=1-x, and y=x-1. 17x3xy dA: R is bounded by y=2-x, y=0, and x 4·-y2 in the first quadrant. d by 50. (x + y) dA: R is bounded by y = 1x1 and y = 4. 51. 1.3x2 dA: Ris bounded by y=0, y=2x+ 4, and y=x3. 52. 1 Rx2yd: R is bounded by y = 0, y = Vx, and y = x-2. 53-56. Volumes Use double integrals to calculate the volume of the following regions the 53. The tetrahedron bounded by the coordinate planes 54· The solid in the first octant bounded by the coordinate planes and 55ãThe segment of the cylinder x2 + y-1 bounded above by the 56. The solid beneath the cylinder y and above the region (x = 0, y = 0, z 0) and the plane z = 8-2x-4y the surface z 1-y-x plane z = 12 + x + y and below by: 0 x + 5
Evaluate each of the following line integrals. (a) c(t) = (2 cost), 2 sin(t)), x dy-y dx, JC 2Ï t (b) x dy + y dx, c(t) = (cos(t), sin(mt)), 2 t 4 (c)yz dx + xz dy + xy dz, where c consists of straight-line segments joining (1, 0, 0) to (0, 1, 0) to (0, 0, 1) (d) x2 dx-xy dy + dz, where c is the parabola z = x2, y = 0 from (-1, 0, 1) to (1, 0, 1)