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Solved: Calculate the integral in Eq.(18.31) Eq.(18.16)
Chapter 18, Problem 85P(choose chapter or problem)
CALC Calculate the integral in Eq. (18.31), \(\int_{0}^{\infty} v^{2} f(v) d v\), and compare this result to \(\left(v^{2}\right)_{a v}\) as given by Eq. (18.16). (Hint: You may use the tabulated integral
\(\int_{0}^{\infty} x^{2 n} e^{-\alpha x^{2}} d x=\frac{1 \cdot 3 \cdot 5 \cdots(2 n-1)}{2^{n+1} \alpha^{n}} \sqrt{\frac{\pi}{\alpha}}\)
where \(\) is a positive integer and \(\alpha\) is a positive constant.)
Equation Transcription:
Text Transcription:
integral_0^infinity v^2 f(v)dv
(v^2)av
integral_0^infinity x^2n e^-alpha x^2 dx=1.3.5...(2n-1)/2^n+1 alpha^n sqrt pi/alpha
n
alpha
Questions & Answers
QUESTION:
CALC Calculate the integral in Eq. (18.31), \(\int_{0}^{\infty} v^{2} f(v) d v\), and compare this result to \(\left(v^{2}\right)_{a v}\) as given by Eq. (18.16). (Hint: You may use the tabulated integral
\(\int_{0}^{\infty} x^{2 n} e^{-\alpha x^{2}} d x=\frac{1 \cdot 3 \cdot 5 \cdots(2 n-1)}{2^{n+1} \alpha^{n}} \sqrt{\frac{\pi}{\alpha}}\)
where \(\) is a positive integer and \(\alpha\) is a positive constant.)
Equation Transcription:
Text Transcription:
integral_0^infinity v^2 f(v)dv
(v^2)av
integral_0^infinity x^2n e^-alpha x^2 dx=1.3.5...(2n-1)/2^n+1 alpha^n sqrt pi/alpha
n
alpha
ANSWER:
Solution 85P
Step 1 of 1:
The Integral formula with n=2 gives