Evaluating a Line
C: boundary of the region lying inside the semicircle
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Calculus (MindTap Course List)
- 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_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_forward
- ulus III |Uni Use Green's Theorem to evaluate the line integral cos (y) dx + x²sin (y) dy along CoS the positively oriented curve C, where C is the rectangle with vertices(0,0), (4, 0), (4, 2) and (0, 2).arrow_forwardLine integrals Use Green’s Theorem to evaluate the following line integral. Assume all curves are oriented counterclockwise.A sketch is helpful. The flux line integral of F = ⟨ex - y, ey - x⟩, where C is theboundary of {(x, y): 0 ≤ y ≤ x, 0 ≤ x ≤ 1}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
- Sind the absolute maximum and the absolute minimum of f(x,y)=2x– 2xy+y² whose domain is the region defined by 0arrow_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_forwardState Green’s theorem. Verify Green’s theorem for P.(xy+ y²)dx + x²dy where C is the closed curve of the region bounded by y = x and y = x².arrow_forwardX Incorrect. Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. fy²dx + 5x dx + 5x²dy, where C is the square with vertices (0, 0), (3, 0), (3, 3), and (0, 3) oriented counterclockwise. y²dx + 5x²dy i 0 eTextbook and Mediaarrow_forwardUse Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. 5x + cos dy - e*)dx, where C is the boundary of the square with vertices (4, 2), (5, 2), (5, 3), and (4, 3). 5x + cos dy - (8y + e dx = (Type an exact answer.)arrow_forwardUse Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. O (5x+ arctany) dy- (4y+ arctan x dx, where C is the boundary of the square with vertices (3, 3), (4, 3), (4, 4), and (3, 4). O (5x+ arctan y²) dy - (4y² + arctan x2) dx = %3D C. (Type an exact answer.)arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,