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Line integrals use Green’s Theorem to evaluate the following line integrals. Assume all curves are oriented counterclockwise. A sketch is helpful.
39. The circulation line
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Calculus: Early Transcendentals and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition) (Briggs, Cochran, Gillett & Schulz, Calculus Series)
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- 2.Proof that any tangent plane for the surface F( F) point = 0 passses through a fixedarrow_forwardUse Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. 8x + cos s-dy- (9y2 + arctan x?) dx, where C is the boundary of the square with vertices (3, 3), (5, 3), (5, 5), and (3, 5). $ 8x + cos - dy - (9y² + arctan x²) dx = D (Type an exact answer.)arrow_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_forward
- ²/F F. dr. (Check the orientation of the curve before applying the theorem.) F(x, y) = (y cos(x) - xy sin(x), xy + x cos(x)), C is the triangle from (0, 0) to (0, 6) to (3, 0) to (0, 0) Use Green's theorem to evaluatearrow_forwardSinx dA where R is the trangle in xy-plane bounded by the x-anise, the line y=x and. the line =arrow_forwardUse Green's Theorem to evaluate F. dr. (Check the orientation of the curve before applying the theorem.) F(x, y) = =(Vx + 4y3, 4x2 + C consists of the arc of the curve y = sin(x) from (0, 0) to (T, 0) and the line segment from (T, 0) to (0, 0)arrow_forward
- Area = Find the area bounded by the parametric curve x = cos(t), y=et, 0 ≤ t ≤ π/2, and the lines y = 1 and x = 0.arrow_forwardUse Green's Theorem to evaluate the line integral along the given positively oriented curve. ∫C xy2 dx + 4x2y dyC is the triangle with vertices (0, 0), (3, 3), and (3, 6)arrow_forwardUse Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwise indicated. ?C(lnx+y)dx−x2dy where C is the rectangle with vertices (1, 1), (3, 1), (1, 4), and (3, 4)arrow_forward
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