Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Sequence and Series
A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.
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before  you get the final answer, please put them back into r and z terms when you get them into trig func

The given integral is expressed as follows: \[ \int_{0}^{R} \frac{r}{(r^2 + z^2)^{3/2}} \, dr \] This mathematical expression represents an integral with the following components: - **Integration Limits**: The integral is evaluated from 0 to \( R \). - **Integrand**: The function being integrated is \( \frac{r}{(r^2 + z^2)^{3/2}} \). - **Numerator**: \( r \) - **Denominator**: \( (r^2 + z^2)^{3/2} \) - **Variable of Integration**: \( dr \) This integral is often encountered in physics, particularly in problems involving fields and potentials, such as calculating the gravitational or electrostatic potential of a circular loop. The form \( (r^2 + z^2)^{3/2} \) in the denominator suggests it is related to the distance in a three-dimensional space.
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Transcribed Image Text:The given integral is expressed as follows: \[ \int_{0}^{R} \frac{r}{(r^2 + z^2)^{3/2}} \, dr \] This mathematical expression represents an integral with the following components: - **Integration Limits**: The integral is evaluated from 0 to \( R \). - **Integrand**: The function being integrated is \( \frac{r}{(r^2 + z^2)^{3/2}} \). - **Numerator**: \( r \) - **Denominator**: \( (r^2 + z^2)^{3/2} \) - **Variable of Integration**: \( dr \) This integral is often encountered in physics, particularly in problems involving fields and potentials, such as calculating the gravitational or electrostatic potential of a circular loop. The form \( (r^2 + z^2)^{3/2} \) in the denominator suggests it is related to the distance in a three-dimensional space.
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