Let R be the region bounded by x + y=1, x - y=1, x+y=3, x-y=-1 evaluate the integral
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Let R be the region bounded by x + y=1, x - y=1, x+y=3, x-y=-1 evaluate the integral s(x+ y)2sen2 (x - y)dA s(x+ y)2sen2 (x - y)dA
17.3 Evaluate the following integral: SSR cosh(x + y)dA where R is the region bounded by x > 0, y = 0 and the line x + 2y = 2.
1. Use polar coordinates to evaluate the double integral dA z2 +y where R is the region in the first quadrant bounded by the graphs x = 0, y = 1, y=4, and y V3z. 1. Use polar coordinates to evaluate the double integral dA z2 +y where R is the region in the first quadrant bounded by the graphs x = 0, y = 1, y=4, and y V3z.
Evaluate the double integral off (x, y) = x + y over the region R bounded by the graphs of x = 13, y = 2, y = 8, and y = 3x-1. Answer:
Evaluate the double integral of f(x, y) = x + y over the region R bounded by the graphs of x = 14, y = 4, y = 8, and y = 3x-1. Answer: Next page
3. Use the transformation u = xy, v = y to evaluate the integral ∫∫R xy dA, where R is the ay region in the first quadrant bounded by the lines y = x and y = 3x, and the hyperbolas xy = 1, xy = 3
2) The region R is bounded by the x-axis and y = V16 – x2. a) (0.75 point) Sketch the bounded region R. Label your graph. b) (0.75 point) Set up the iterated integral to solve for the area of the bounded region using either the Rx region or Ry region. Do not integrate. c) (1.25 point) Evaluate the integral using polar coordinates for the region R. S sec(x2 + y2) tan(x2 + y2) da R
2) The region R is bounded by the x-axis and y = V16 – x2 a) (0.75 point) Sketch the bounded region R. Label your graph. b) (0.75 point) Set up the iterated integral to solve for the area of the bounded region using either the Rx region or Ry region. Do not integrate. c) (1.25 point) Evaluate the integral using polar coordinates for the region R. S sec(x2 + y2) tan(x2 + y2) da R
3. Let region R be bounded by y = 2x - x? and y = 0 on (0,2). Setup the definite integral(s) that represents the volume of the solid generated by rotating region about the y-axis. Draw a sketch to interpret your results.
1 R 12. Use the transformation T: u = -x and very to evaluate the integral [jx?dA where R is the region bounded on the xy-plane by the ellipse 9x + 4y = 36. . Let S be the image of Runder T on the uv-plane. Sketch regions and S. Set up the integral 7as an iterated integral of a function f(u, v) over region S. Use technology to evaluate the integral. Give the exact answer. R S Y
1/3 x + y 7. Consider dA where R is the region bounded by the triangle with vertices (0,0), (2,0), V= x+y X-y and (0,-2). The change of variables u=- defines a transformation T(x,y)=(u,v) from the xy-plane 2 to the uv-plane. (a) (10 pts) Write S (in terms of u and v) using set- builder notation, where T:R→S. Use T to help you sketch S in the uv-plane by evaluating T at the vertices. - 1 a(u,v) (b) (4 pts)...