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How do you calculate an integral to find a region bounded by graphs?

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Calculate the Integral.

8. Let R be the region bounded by the graphs of x + y = 1, x + y = 2, 2x - 3y = 2, and 3x - 3y = 5. Use change of variables, x = (1/c)(3u + v), y = (1/c)(2u - v), to evaluate the double integral of (2x - 3y)dA.

10. Using multiple integration and a convenient coordinate system to find the volume of the solid inside the graphs of r^2 + z = 16, z = 0, and r - 2sin(theta). Calculate the integral by hand.

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This provides an example of solving an integral by cylindrical coordinates in an attached Word document.

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