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(c) f(x, y) = ysin(x), R is the triangle with vertices at (0, 0), (1,0), and (1, 4). (d) f(x, y) = x3y, R is
(c) f(x, y) = ysin(x), R is the triangle with vertices at (0, 0), (1,0), and (1, 4). (d) f(x, y) = x3y, R is the region bounded by y = x2 - 1 and y = -r + 1. (e) f(x, y) = vx2 + y2, R is the region inside the cardioid r = 4(1 - sin(0)). (f) f(x, y) = e (x ty"), R is the region bounded by x2 + y? = 1 and x2 + y? = 9. 2. Calculate the integral / (x2 - y?)?dydx by converting to polar coordinates. (Hint: After converting to polar coordinates, there might be a trig identity that can help you simplify the integrand)
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