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- Compute the line integral∫C [2x3y2 dx + x4y dy]where C is the path that travels first from (1, 0) to (0, 1) along the partof the circle x2 + y2 = 1 that lies in the first quadrant and then from(0, 1) to (−1, 0) along the line segment that connects the two points.Find the line integral of C in two ways; A) Directly. B) Using Green's theorem. C eata formed by the line segment from (0. 0) to (1, 2), followed by the arc from (1, 2) to (0, 3) from y = 3 - x2, followed by the line segment from (0, 3) to (0. 0) whereCompute the line integral of F(x, y) = (x3, 4x} along the path from A to B in Figure 19. To save work, use Green's Theorem to relate this line integral to the line integral along the vertical path from B to A.
- Calculate the double integral. 6x/1+xy dA, R=[0,6]x[0,1]Evaluate the line integral ∫Cydx+xdy along the curve y=x2 from the point O(0,0) to the point A(1,1) (Figure 3 above).Evaluate both sides of the equation to verify Green's Theorem for the integral (image attached) Where C: line segment from (0,0) to (2,0) from (2,0) to (1,4) and from (1,4) to (0,0)
- Evaluate the line integrals using the Fundamental Theorem of Line Integrals: ∫c (yi+xj)*dr Where C is any path from (0,0) to (2,4).I don't understand why the double integral of z dA over region D turns into [(64-4r^2)^(1/2)-(-(64-4r^2)^(1/2)]rdrdtheta, instead of just (64-4r^2)^(1/2) rdrdtheta since R {(r,theta) | 0 <= r <= 2; 0 <= theta <+ 2pi}.Compute the line integral of f(x)=2x over the curve y=x^2 from (0,0) to (1,1)