
8. Sketch the region of integration and evaluate the integral re dx dy, where G is the region bounded by 0,1, -o,y-
8. Sketch the region of integration and evaluate the integral re dx dy, where G is the region bounded by 0,1, -o,y-
Evaluate the iterated integral: 5 L, Vx+4y dx dy Answer:
13. Let D be a region in the xy plane. Let A-dx dy JJ D Let aD be the region in which every point (x, y) in D is replaced by (az, ay) for α 0. Interpret the double integral as a Riemann sum and find the area of aD in terms of A and a.
Use the given transformation to evaluate the integral. -5x dx dy where R is the parallelogram bounded by the linesy-x+1, y-x +4 y#2x+2y»2x + 5 A) -5 B) 10 C)5 D)-10 32) y+ x where R is the trapezoid with vertices at (6,0), ,0).。. 6), (0.9) 45 45 B) ÷ sin l 45 C) sin 2 45 A) sin 2
Use the given transformation to evaluate the integral. -5x dx dy where R is the parallelogram bounded by the linesy-x+1,...
Evaluate the integral cosh(r)dx dy dz Jo o
Evaluate the integral cosh(r)dx dy dz Jo o
evaluate using green's theorem line integral (4x^3+sin y^2)dy-(4y^3+cosx^2)dx, where C is the boundary of the region x^2+y^2 greater equal to 4
(1) Evaluate S SIS "Jo dzdydi B. Evaluate JJ y dA where D is the region bounded by xay and y = 2 - X.
5) Use Green's Theorem to evaluate | (xy)dx + (y2 +4)dy where is the cardoid r = 1 + sine OSOS 21 с
Consider the region R shown in the figure and write an iterated integral of a continuous function over R. Choose the correct iterated integral below OA Oc. OD JJ fx.y) dy dx S Study de Consider the region R shown in the figure and write an erated integral a continuous function for Choose the correct terated integral below JJ Roxy) dy dx JJ x) dx dy
10 Given the double integral 4(x+ y)e dy dx, where R is the triangle in the xy-plane with vertices at (-1, 1), (1, 1) and (O,0). Transform this integral into J g(u.)dv du by the transformations given by 스叱制一想ル r}(u+v), y (u + v), y =-(u-v). Then, Evaluate the integral." (u-v). Then, Evaluate the integral. r
10 Given the double integral 4(x+ y)e dy dx, where R is the triangle in the xy-plane with vertices at (-1, 1), (1, 1)...