8. Evaluate the double integral S Sp y³dA where A is the triangular region with vertices (0, 2), (1,1) and (3,2).
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A: we have to find given double integral
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Q: 2. Evaluate the double integral. SSp(x – 2y) dA, D = {(x, y)|1< x< 3, (1+x) < y < 2x} а.
A: As you post multiple question according to guideline I only solve the first one. Please request your…
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Solved in 3 steps with 3 images
- How do I sketch the region R that is bounded by the xy and yz planes, and the planes z=6, y=2x, and y= 3. How would I also compute ||R||?Evaluate the line integral ∫Cx^3z ds, where C is the line segment from (0,3,8) to (8,4,6).Evaluate the double integral ∬D2xydA,∬D2xydA, where DD is the triangular region with vertices (0,0),(0,0), (1,2),(1,2), and (0,3).
- What is the absolute extrema of Q(y,z) = y2z2 on a region with vertices at the points (0,0), (0,4) and (4,0)?Let D be the triangular region in the xy-plane with vertices (1,0), (0.1) and (3/2, 1/2) Use a suitable change of variables to calculate the integral (image)Use Green’s Theorem to evaluate around the boundary curve C of the region R, where R is the triangle formed by the point (0, 0), (1, 1) and (1, 3).
- Find the volume of the solid S under z = 3 + 2 cos x^2 and restrictedby a triangle in the xy-plane with the vertices (0, 0),(6, 0) and (6, 2).3.1 Use the Cauchy integral formulas to evaluate the ∮c eizcos z/ z2(2z -3π) dz, where C is the region covered by circle |z - 2| = 3.Find the integral of f(x, y, z) = z over the region R, where R is the pyramid with a square base having vertices (1, 1, 0), (1, −1, 0), (−1, −1, 0), and (−1, 1, 0) and with its top at (0, 0, 2).