Evaluate the following double integrals. (a) f(z - y)dA, where R= (b) ||e/vdA, where R =...

   

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Evaluate the following double integrals. (a) f(z - y)dA, where R= (b) ||e/vdA, where R = {(x, y)|1 y 2, y x y}. R (c) J -dA, where R = {(x, y) | 0 x1, 0y }. 2y x +1 R (d) siny dA, where R = {(x, y) |0 x y, 0 y 2}. Evaluate the following double integrals. (a) (b) R R 9 = {(21)135254 SUS=}. (x-y)dA, where R=(x, y) | 3 x 4, z cos y dA, where R is the region bounded by y = 0, y = 2 and x = 1. (2 + 2y)dA, where R is the region bounded by y = 1- x, y = 1 + x and z-axis. (24-2y)dA, where R is the region bounded by the lines x = -1, x= 1 and the curves y=x, y = -x. (d) !! (2x + y)dA, where R is the region bounded by x+y= 2, x = y and y-axis. R 3. (c) R Evaluate the following double integrals by reversing the order of integration. r9 ( fedy dz. (b) /4-y (c) (d) 4. Use double integral to find the following areas: (a) bounded by the parabola y = 6x - x and the line y = x. bounded by the line y = 2x and the curve y = 2x. (b) (c) bounded by the lines x = -1, x = 2, y = x and the parabola y = x + 1. 4 (d) bounded between the curve y = and the line y =5-x. I (e) bounded by the lines y = 12- x, y = 4x + 12 and the parabola y = x. (x + y) dx dy. y y cos 2 dz dy. -dy dx. (f) bounded by the lines y = -2, y = 3, y = x - 3 and the parabola z = -. (g) bounded by y = sin z and y = cos a for 0 x 2. Evaluate the following double integrals. (a) f(z - y)dA, where R= (b) ||e/vdA, where R = {(x, y)|1 y 2, y x y}. R (c) J -dA, where R = {(x, y) | 0 x1, 0y }. 2y x +1 R (d) siny dA, where R = {(x, y) |0 x y, 0 y 2}. Evaluate the following double integrals. (a) (b) R R 9 = {(21)135254 SUS=}. (x-y)dA, where R=(x, y) | 3 x 4, z cos y dA, where R is the region bounded by y = 0, y = 2 and x = 1. (2 + 2y)dA, where R is the region bounded by y = 1- x, y = 1 + x and z-axis. (24-2y)dA, where R is the region bounded by the lines x = -1, x= 1 and the curves y=x, y = -x. (d) !! (2x + y)dA, where R is the region bounded by x+y= 2, x = y and y-axis. R 3. (c) R Evaluate the following double integrals by reversing the order of integration. r9 ( fedy dz. (b) /4-y (c) (d) 4. Use double integral to find the following areas: (a) bounded by the parabola y = 6x - x and the line y = x. bounded by the line y = 2x and the curve y = 2x. (b) (c) bounded by the lines x = -1, x = 2, y = x and the parabola y = x + 1. 4 (d) bounded between the curve y = and the line y =5-x. I (e) bounded by the lines y = 12- x, y = 4x + 12 and the parabola y = x. (x + y) dx dy. y y cos 2 dz dy. -dy dx. (f) bounded by the lines y = -2, y = 3, y = x - 3 and the parabola z = -. (g) bounded by y = sin z and y = cos a for 0 x 2.