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Verifying Green’s TheoremIn Exercises 5–8, verify Green’s Theorem by evaluating both
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C: boundary of the region lying between the graphs of
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Chapter 15 Solutions
Calculus (MindTap Course List)
- Evaluate z in rectangular formarrow_forwardEvaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 5 y²dx + 6 x²dy, where C is the square with vertices (0, 0), (2, 0), (2, 2), and (0, 2) oriented counterclockwise. f 5 y²dx + 6x²dy =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
- Evaluating line integral, can u add explanation to question solutionarrow_forwardEvaluate 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_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
- (b) Evaluate the line integral Jo dzalong the simple closed contour C shown in the diagram. -2 -1 2j o 1 2arrow_forwardUse Green's Theorem to evaluate the following line integral. Assume the curve is oriented counterclockwise. A sketch is helpful. + 2, • dr, where C is the boundary of the rectangle with vertices (0,0), (2,0), (2,4), and (0,4) Play + 2,32 - 7) • dr = (Type an exact answer.)arrow_forwardEvaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 2y dx + 3x²dy, where Cis the square with vertices (0, 0), (2, 0), (2, 2), and (0, 2) oriented counterclockwise. O 2y dx + 3x²dy = iarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,