Concept explainers
Evaluating a Line
C: boundary of the region lying inside the semicircle
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EBK CALCULUS: EARLY TRANSCENDENTAL FUNC
- 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_forwardUse Green's Theorem to evaluate the line integral. | 3x2eY dx + eY dy C C: boundary of the region lying between the squares with vertices (1, 1), (-1, 1), (-1, -1), (1, -1) and (8, 8), (-8, 8), (-8, -8), (8, -8)arrow_forwardef 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_forward
- Evaluate 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_forwardUse Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. $c a15x+ 5x+ In 5y)dy - (8y² + arctan x2) dx, where C is the boundary of the square with vertices (0, 5), (2, 5), (2, 7), and (0,7), C $c (5x + In 5y)dy – (8y? + arctanx?) dx = | | C (Type an exact answer.)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_forward
- Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. (9x + In 9y)dy - (8y + ex ) dx, where C is the boundary of the square with vertices (4, 4), (7, 4), (7, 7), and (4, 7).arrow_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 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
- (a) Let f(z) = (z +4- i(24 + 5z) Using CRT, evaluate the integral of(e)dz, where the contour C is the circle z + 4| = 2. z9 +5 (b) Evaluate the domain of the function h(z) = 3 %3D z2 +i Windows buii انتقل إلى الإعدادت لتند コ )园中arrow_forwardVerify: Green's theorem in the plane for f(2x-y³)dx-xydy, where C is the boundary of the region enclosed by the circles x² + y² = 1 and x² + | x² + y² = باتخیرarrow_forwardEvaluate the line integral using Green's Theorem and check the answer by evaluating it directly. P y*dx + 2x²dy, where C is the square with vertices (0, 0), (3, 0), (3, 3), and (0, 3) oriented counterclockwise. P y'dx + 2x*dy :arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,