
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Change the Cartesian
![## Converting Cartesian Integrals to Polar Integrals
### Problem Statement
Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.
\[
\int_{0}^{\ln 9} \int_{0}^{\sqrt{(\ln 9)^2 - y^2}} e^{\sqrt{x^2 + y^2}} \, dx \, dy
\]
---
### Conversion to Polar Coordinates
Change the Cartesian integral into an equivalent polar integral.
\[
\int_{0}^{\ln 9} \int_{0}^{\sqrt{(\ln 9)^2 - y^2}} e^{\sqrt{x^2 + y^2}} \, dx \, dy = \int_{0}^{\square} \int_{0}^{\square} e^{r} \, r \, dr \, d\theta
\]
**Note**: (Type exact answers, using \(\pi\) as needed.)](https://content.bartleby.com/qna-images/question/74590d71-03c8-490e-9c40-f641d63c995d/98fc82c4-1875-4b72-bd3d-74d2802645dd/58jeq0m_thumbnail.png)
Transcribed Image Text:## Converting Cartesian Integrals to Polar Integrals
### Problem Statement
Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.
\[
\int_{0}^{\ln 9} \int_{0}^{\sqrt{(\ln 9)^2 - y^2}} e^{\sqrt{x^2 + y^2}} \, dx \, dy
\]
---
### Conversion to Polar Coordinates
Change the Cartesian integral into an equivalent polar integral.
\[
\int_{0}^{\ln 9} \int_{0}^{\sqrt{(\ln 9)^2 - y^2}} e^{\sqrt{x^2 + y^2}} \, dx \, dy = \int_{0}^{\square} \int_{0}^{\square} e^{r} \, r \, dr \, d\theta
\]
**Note**: (Type exact answers, using \(\pi\) as needed.)
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