Stuck with Integeration by substitution Watch

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driving_seat
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#1
Report Thread starter 13 years ago
#1
Hi guyz.

I am stuck with following question of Integeration by substitution (P3). I was wondering if anyone can help me out.

Q1. Evaluaute by using substitution

∫ x*e^(-0.5x2)
-∞

Q. Use a substitution, followed by a change of letter in the integrand, to show that if σ>0,


-∞ e^(-x²/2σ²)dx=σ∫-∞ e^[-1/(2x²)]dx



Thanx
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Gaz031
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Report 13 years ago
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Q1. Evaluaute by using substitution

∫ x*e^(-0.5x2)
-∞
\int_{-\infty}^{\infty} xe^{-0.5x^2} dx = [-e^{-0.5x^2}]_{-\infty}^{\infty} \\

= \lim_{X \rightarrow \infty} -e^{-0.5X^{2}}+e^{-0.5X^{2}} \\

= 0

Q. Use a substitution, followed by a change of letter in the integrand, to show that if σ>0,
∫∞-∞ e^(-x²/2σ²)dx=σ∫∞-∞ e^[-1/(2x²)]dx
You could try working backwards, writing the term on the right as
Unparseable or potentially dangerous latex formula. Error 4: no dvi output from LaTeX. It is likely that your formula contains syntax errors or worse.
\int_{-\infty}^{\infty} e^{lna-\frac{1}{2v^{2}} dx
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