a) Change the following double integral into polar coordinates and evaluate it \

Question

a) Change the following double integral into polar coordinates and evaluate it "Use the formula(picture) to answer the question"

b)Explain why "Use the formula (picture) to answer the question"

c)Explain why the answers to parts a and b give the formal we want

The problem is from the book "Calculus" Multivariable written by McCallum, Hughes and Gleason(5th edition), its in chapter 16 in the"Projects for Chapter 16" Section, question number 1(the last part of the chapter is where you;ll find it)

I have a test on this tomorrow and I really need a clear answer and explanation to this question

Thank You!!!

Explanation / Answer

To change from Cartesian coordinates (x,y) to Polar Coordinates (r, theta), you need to perform the following substitutions: x = r*cos(theta) y = r*sin(theta) and: r = sqrt(x^2+y^2) theta = arctan(y/x) The general form of the integral substitution is: double integral[f(x,y)dydx] = double integral[f(r*cos(theta), r*sin(theta))*r*dr*d(theta)] Below is a website with some examples

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