Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region lying between the graphs of y = 0 and y = 1 - x2
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- Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. $(5) (5x+ sinh y)dy - (3y² + arctan x²) dx, where C is the boundary of the square with vertices (1, 3), (2, 3), (2, 4), and (1,4). false (Type an exact answer.) (5x + sinh yldy – (3y® + arctan x an x²) dx = dx = ...Use Green's Theorem to evaluate the line integral. dx + (e-r12 + x) dy -y2/2 - C: boundary of the region lying between the graphs of the circle x = 10 cos(0), y = 10 sin(8) and the ellipse x = 5 cos(0), y = 2 sin(8)Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. (7x + sinh y)dy - (4y + arctan x) dx, where C is the boundary of the square with vertices (1, 3), (2, 3), (2, 4), and (1, 4). (7x + sinh y)dy - (4y + arctan x) dx = (Type an exact answer.)
- Find a simple closed curve C with counterclockwise orientation that maximizes the value of 1 $ 3x³ dx + ( 36.x - 32x²) dy. O The integral doesn't depend on the form of C. OC is the triangle with vertices (0, 0), (6, 0), and (0, 6). OC is the square with vertices (0, 0), (6, 0), (6, 6), and (0, 6). O C is a circle of radius 6 with the center at (6, 6). OC is a circle of radius 6 with the center at the origin.5) Using Green's theorem, convert the line integral f.(6y? dx + 2xdy) to a double integral, where C is the boundary of the square with vertices ±(2, 2) and ±(2, -2). ( do not evaluate the integral)Use Green's Theorem to evaluate the line integral along the given positively oriented curve. (3y + 5evx) dx + (10x + 9 cos(y²)) dy C is the boundary of the region enclosed by the parabolas y = x² and x = y² -
- Use Green's Theorem to evaluate the line integral along the given positively oriented curve. xe-5x dx + (x* + 2x?y²) dy хе Cis the boundary of the region between the circles x2 + y2 = 9 and x2 + y2 = 25Use Green's theorem to evaluate the line integral along the given positively oriented curve. | (3y + 7evx) dx + (8x + 7 cos(y?)) dy, Cis the boundary of the region enclosed by the parabolas y = x? and x = y?Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region lying between the graphs of y = 0 and y = 1 - x²
- // y - 2)? y2 + 1 Let D = {(x, y) E R?; |æ|+ ly – x| < 1} and I = -dxdy. (i) Sketch the graph of the domain D and then use it to give a change of variables u and v. (ii) Evaluate the double integral T.Calculate the integral of f(x, y) = (x² + y²)¯ -3/2 over the region x² + y² ≤ 100, x + y ≥ 10 by changing to polar coordinates. (Use symbolic notation and fractions where needed.) Jox (x² + y²)-3/2dA =The graph of g consists of two straight lines and a semicircle as shown in the figure. (b) 0 30 10 1 y 20 10 0 Evaluate each integral by interpreting it in terms of areas. (a) 9(x) dx g(x) dx y = g(x) g(x) dx 20 35 X