Match each double integral in polar with the graph of the region ofintegration.7π/4? v 1.S.f(r, 0) r de drJ3π/4+27? 2.S³ ²* f(r, 0) r dr do3π/4[? ~) 3. [20/1 1/².f(r, 0) r dr de-π/4 √22 3π/4?4.f(r, 0) r de dr•2? ✓ 5.Som fºr f(r, 0) r dr de3π/22π?6. *** (r. 9) r dr d9f(r, 0)03π/2? ✓7. [2672 [² f(x,f(r, 0) r dr de3π/4JO+2 p3π/4? ✓8. ² m/s f(r, 0) r do dr-TT/21414ADGBEHсF

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Answered: Match each double integral in polar…

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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1)Sketch the solid obtained by rotating the region bound byy=2√x and y=x, about the line x =−2. 2)Write the expression for the area of a representative washer 3)Set up and solve the definite integral used to calculate the volume of the solid in (1)
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Say that you need to compute a double integral of the function f(x,y)=xy over the region D bounded by the x-axis, y=x, x2+y2=1, and x2+y2=16. Explain in words and/or show in a picture why this would be (unnecessarily) complicated in Cartesian coordinates. Then, setup and evaluate the integral using polar coordinates.
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