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Evaluating a Line
C: boundary of the region lying between the graphs of
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CALCULUS EARLY TRANSCENDENTAL FUNCTIONS
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- ef F Use Green's Theorem to evaluate nds, where F = (√x + 4y, 2x + 4y) C' is the boundary of the region enclosed by y = 5x - x² and the x-axis (oriented positively).arrow_forwardEvaluate the line integral using Green's Theorem and check the answer by evaluating it directly. ²dx + 2x²dy, where C is the square with vertices (0, 0), (3, 0). (3, 3), and (0, 3) oriented counterclockwise. fy²dx + 2x²dy =arrow_forward(x+y)e**-dA , where R is the rectangle enclosed by the lines r- y = 0, R x - y = 2, x + y = 0 and r+y = 3. Transform R into uv plane by making an appropriate change of variables in order to find the integral. (a) Plot R in both ry and uv planes. (b) Find the Jacobian of the transformation (c) Evaluate the integral using the transformationarrow_forward
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