Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 

## 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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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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