Originally Posted by

**TheNerdyGinger**
Hello. On this problem shown in the attached image, I have to combine two double integral sums into one double integral.

15. This sum of two double integrals may be written as one double integral.

. . . . .[tex]\color{blue}{ \displaystyle \int_0^3\, \int_0^{\frac{4x}{3}}\, f(x,\, y)\, dy\, dx\, +\, \int_3^5\, \int_0^{\sqrt{\strut 25\, -\, x^2\,}}\, f(x,\, y)\, dy\, dx }[/tex]

What is this one double integral?

Answer:

. . . . .[tex]\color{green}{ \displaystyle \int_0^4\, \int_{\frac{3y}{4}}^{\sqrt{\strut 25\, -\, y^2\,}}\, f(x,\, y)\, dx\, dy }[/tex]

...or:

. . . . .[tex]\color{green}{ \displaystyle \int_0^{0.927}\, \int_0^5\, f(r,\, \theta)\, r\, dr\, d\theta }[/tex]

Looking at the answer, it seems one easy way to do it is to convert to polar coordinates. How would I go about doing this?
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