Work Problem 1 (With integrity statement] ( Let R be the region bounded by y-x+2, y=0, and x=2. Draw the region R, and evaluate the following double integral. +2y dA=?
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A: Explanation of the answer is as follows
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Q: Q2) Convert the polar function r tan20 to cartesian.
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Q: Q3) Evaluate triple integral dz dy dx.
A: A detailed solution is given below
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- If I let the boundary E be given by dE : (x^2) / 9 + (y^2) / 4 = 1. How do I compute the double integral over the region E of (2/3)*x^2 + (3/2)*y^2 dA17. Region bounded by y = 2x, y = x and x = 2. Rotate about: (a) the y-axis (b) x = 2 (c) the x-axis (d) y = 4Question #19.Find the centroid of the region bounded by the graphs of y=x,x=1/y^2 and y=2
- Set up an integral representation of the area of the region bounded by: x=y2 ,x+y=2, y=015) Sketch the region of integration and evaluate the integral:∫30∫√9−x20(x3+xy2)dy dx5.) Sketch the region of integration and write an equivalent double integral with the order of integration reversed and then evalute: ∬(x+y) dx.dy (0-3; 1-e^y)
- Sketch the region enclosed by y = e 3 x y = e 3 x , y = e 8 x y = e 8 x , and x = 1 x = 1 . Decide whether to integrate with respect to x x or y y . Then find the area of the region.4. Evaluate the double integral over rectangle S, xycosy dA, R:[-1,2] x [0, Pi]43. If the x-coordinate of the centroid of the region that lies under the graph of a continuous function where a <= x <= b show that int a ^ b (cx+d)f(x)dx=(c overline x +d) int a ^ b f(x)dx
- integrate ƒ over the given region. ƒ(x, y) = x2 + y2 over the triangular region with vertices (0, 0), (1, 0), and (0, 1)12. Given that f(x,y) = 1- x and D is the triangular region with vertices (0,0), (0,2), (6, 2). Set up two different integrals which evaluate the volume between the region D and the surface f(x, y) in two different ways. Do NOT evaluate these two integrals.HW 3 & 4 Dr. Jatit J. Shukur Q1: Find the volume of the colid generated by the region bounded by y= /X and the limes 3= 1, x= 6 by revohving about the line y = 1