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Evaluating a Line
C: boundary of the region lying between the graphs of
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Chapter 15 Solutions
EBK CALCULUS: EARLY TRANSCENDENTAL FUNC
- Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. ∮C6 y2dx+3 x2dy∮C6 y2dx+3 x2dy, where CC is the square with vertices (0,0)(0,0), (3,0)(3,0), (3,3)(3,3), and (0,3)(0,3) oriented counterclockwise.arrow_forwardLine integrals Use Green’s Theorem to evaluate the following line integral.Assume all curves are oriented counterclockwise.A sketch is helpful.arrow_forwardUse Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise. 3 In(3 + y) dx - -dy, where C is the triangle with vertices (0,0), (6, 0), and (0, 12) ху 3+y ху dy = 3 In(3 + y) dx - 3+ yarrow_forward
- 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_forwardThe figure shows a region R bounded by a piecewise smooth simple closed path C. R (a) Is R simply connected? Explain. (b) Explain why f(x) dx + g(y) dy = 0, where f and g are differentiable functions.arrow_forwardEvaluate the integralarrow_forward
- Use Green's Theorem to evaluate the following integral Let² dx + (5x + 9) dy Where C is the triangle with vertices (0,0), (11,0), and (10, 9) (in the positive direction).arrow_forwardLine integrals Use Green’s Theorem to evaluate the following line integral. Assume all curves are oriented counterclockwise.A sketch is helpful.arrow_forwardUse Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. $c (5x + sinh y)dy − (3y² + arctan x²) dx, where C is the boundary of the square with vertices (1, 3), (4, 3), (4, 6), and (1, 6). $c (Type an exact answer.) - (3y² + arctan x² (5x + sinh y)dy – nx²) dx dx = (arrow_forward
- Use Green's Theorem to evaluate the line integral along the given positively oriented curve. √(3y + 5e√x) dx + (8x + 3 cos(y²)) dy C is the boundary of the region enclosed by the parabolas y = x² and x = = y² Need Help? Read It Watch It Master Itarrow_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_forwardsolve. show workarrow_forward
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