Question 1(a) Evaluate the integral [x²dA where E is the region between the curve y = -x²+6x andthe line y=-2x. Draw the region E. Is it a type I or type II region?(b) Use polar coordinates to evaluate the integral [ xy² dA where E is the region enclosed byEthe circles centered at the origin with radius 1 and 3, the line y=x, and the y-axis in the 3rdquadrant. Sketch the region.(c) Evaluate the integralbox E=[-3, 4] x [-4, 5] x [-4, 5]f(x,y,z)dV where f(x,y,z) = 3y + 6z and E is the rectangular

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Answered: (a) Evaluate the integral [x²dA where E…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(a) Evaluate the integral [x²dA where E is the region between the curve y=-x²+6x and the line y=-2x. Draw the region E. Is it a type I or type II region?