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- Since the R integration region is the region bounded by the hyperbolas x2 - y2 = 1, x2 - y2 = 9, xy = 4 and xy = 2 in the first region, with the help of u = xy and v = x2 - y2 transformation ∫∫R ( x2 + y2) dA What is the value of the integral?a) 0b) -7c) 7d) 8e) noneintegrate ƒ over the given region. ƒ(x, y) = x2 + y2 over the triangular region with vertices (0, 0), (1, 0), and (0, 1)Solve the problem with complete solution and draw the figure. Determine the ordinate of the centroid of the area bounded by the curve x2 = 8y and the line 2x – y = 0.
- Evaluate the line integral ∫AB(x+y)dx+xdy for two paths of integration: AB is the line segment from A(0,0) to B(1,1); AB is the parabola y=x2 from A(0,0) to B(1,1).[xcsc (y/x) - y]dx + xdy = 0 TEST FOR HOMOGENEITY OF DEGREE N: Let:F(x,y) = M(x,y)DX + N(x,y)dy F(rx,ry) = R^n(x,y)Find the maximum and minimum values of the function f (x,y) = x2 + 2y2 - x2y2 . On the region D = {(x,y) | x2+y2 <= 4 , y >= 0}.