Approximation In Exercises 3-6, approximate the
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Multivariable Calculus (looseleaf)
- Solve using greens theoremarrow_forwardUse Green's theorem to calculate the integral - dx + dy, where C is a rectangle with vertices (–1,1), (2, 1), (2, 5), and (–1,5), oriented counterclockwise.arrow_forwardLet S = 0 (D), where D = {(u, v): u²+ v² ≤ 9,u ≥ 0, v ≥ 0} and ℗ (u, v) − (2u + 1,u − v, 3u + v). (a) Calculate the surface area of S. (Express numbers in exact form. Use symbolic notation and fractions where needed.) area (S) = Incorrect 9√6T 2 (b) Evaluate (4x – 4y) dS. Hint: Use polar coordinates. (Express numbers in exact form. Use symbolic notation and fractions where needed.) (4x - 4y) dS - 18√618+]arrow_forward
- 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_forwardPlease help solve for the problem provided in the photo belowarrow_forwardEvaluate Y X R y + x where R is the triangular region with vertices (0,0), (0, 1), and (1, 0). sin dA,arrow_forward
- Find shaded area ? 8.1)arrow_forwardLet C be the square with vertices (0, 0), (1, 0), (1, 1), and (0, 1) (oriented counter-clockwise). Compute the line integral: y² dx + x² dy two ways. First, compute the integral directly by parameterizing each side of the square. Then, compute the answer again using Green's Theorem.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage