(1) Evaluate S SIS "Jo dzdydi B. Evaluate JJ y dA where D is the region...
Evaluate I = JJ, že 2x1 da, where D is the rectangular region described by O sxs 4 In (5), and 4 sys8. (Type an exact answer in simplified form.)
9. (10 points) Evaluate S SR(2x2 - xy - y2)dA, where R is the region bounded by y = -2x +4, y = -2x + 7, y = x - 2, and y = 1 +1.
1. Use polar coordinates to evaluate the double integral dA z2 +y where R is the region in the first quadrant bounded by the graphs x = 0, y = 1, y=4, and y V3z. 1. Use polar coordinates to evaluate the double integral dA z2 +y where R is the region in the first quadrant bounded by the graphs x = 0, y = 1, y=4, and y V3z.
Let R be the region bounded by x + y=1, x - y=1, x+y=3, x-y=-1 evaluate the integral s(x+ y)2sen2 (x - y)dA s(x+ y)2sen2 (x - y)dA
2. (35pt)Evaluate SS 3xy²dA, where R is the region bounded by the graphs of y = -x and y = x2, x > 0 and the graph of x = = 1. R
5x cos(y3)dA Where D is the region bounded by y = 2, y = -x and the y axis.
1/3 x + y 7. Consider dA where R is the region bounded by the triangle with vertices (0,0), (2,0), V= x+y X-y and (0,-2). The change of variables u=- defines a transformation T(x,y)=(u,v) from the xy-plane 2 to the uv-plane. (a) (10 pts) Write S (in terms of u and v) using set- builder notation, where T:R→S. Use T to help you sketch S in the uv-plane by evaluating T at the vertices. - 1 a(u,v) (b) (4 pts)...
4. Evaluate ſfx da, where D is the region in the first quadrant that lies between = 1 and x + y = 2 D
Determine the following integral where D is the region bounded by x = y, y = 0 and x+y= 2. S S (1 + xy") da = D [3 points]
y, dA where D is the solid in Octa 2 +--4 and the plane y-i. Evaluate by the cylinder nt I bounded JJD y, dA where D is the solid in Octa 2 +--4 and the plane y-i. Evaluate by the cylinder nt I bounded JJD