(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate the integral [tex]\int {\int\limits_R {\left( {x + y} \right)\,dA} } [/tex] where R is the region that lies to the left of the y-axis between the circles [tex]x^2 + y^2 = 1[/tex] and [tex]x^2 + y^2 = 4[/tex] by changing to polar coordinates.

2. Relevant equations

x=r cos theta

y=r sin theta

3. The attempt at a solution

my effort:

[tex]\begin{array}{l}

r_{inner} = \sqrt 1 = 1,\,\,r_{outer} = \sqrt 4 = 2 \\

R = \left\{ {\left( {r,\theta |1 \le r \le 4,\,\frac{{3\pi }}{2}\,\theta \le \pi } \right)} \right\} \\

x = r\cos \left( \theta \right),\,\,\,y = r\sin \left( \theta \right) \\

\int\limits_1^2 {\int\limits_{\pi /2}^{3\pi /2} {\left( {r\cos \left( \theta \right) + r\sin \left( \theta \right)} \right)\,d\theta \,dr} } \\

\end{array}[/tex]

The solution shows an extra instance of r in the integral. If the original question is for (x+y) then why isn't it simply r cos + r sin, rather than r(r cos + r sin)?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Evaluate Double integral

**Physics Forums | Science Articles, Homework Help, Discussion**