Prove that ∫x^me^-ax^ndx for x ∈ [0, ∞] = 1/na^((m + 1)/n) Γ(m + 1/n), - Sarthaks eConnect | Largest Online Education Community
![integral from -infinity to infinity of exp(-x^2) is sqrt(pi). I always found this very elegant. | Mathematics geometry, Physics and mathematics, Studying math integral from -infinity to infinity of exp(-x^2) is sqrt(pi). I always found this very elegant. | Mathematics geometry, Physics and mathematics, Studying math](https://i.pinimg.com/originals/d7/1d/08/d71d08985000300bde926b5739144e53.jpg)
integral from -infinity to infinity of exp(-x^2) is sqrt(pi). I always found this very elegant. | Mathematics geometry, Physics and mathematics, Studying math
![SOLVED: 46. Find the following Integrals: (a) fooo e U2 dx (b) fx xe ax? dx (c) fwo T?e-ax' dx (d) f:= sin(0)do (e) f+= sin? (0)d0 (€) f-F cos(0)de (g) f+5 SOLVED: 46. Find the following Integrals: (a) fooo e U2 dx (b) fx xe ax? dx (c) fwo T?e-ax' dx (d) f:= sin(0)do (e) f+= sin? (0)d0 (€) f-F cos(0)de (g) f+5](https://cdn.numerade.com/ask_images/7a13f9d162fd40e38bee551874fc276e.jpg)
SOLVED: 46. Find the following Integrals: (a) fooo e U2 dx (b) fx xe ax? dx (c) fwo T?e-ax' dx (d) f:= sin(0)do (e) f+= sin? (0)d0 (€) f-F cos(0)de (g) f+5
![calculus - Evaluation of Gaussian integral $\int_{0}^{\infty} \mathrm{e }^{-x^2} dx$ - Mathematics Stack Exchange calculus - Evaluation of Gaussian integral $\int_{0}^{\infty} \mathrm{e }^{-x^2} dx$ - Mathematics Stack Exchange](https://i.stack.imgur.com/kEv1D.png)
calculus - Evaluation of Gaussian integral $\int_{0}^{\infty} \mathrm{e }^{-x^2} dx$ - Mathematics Stack Exchange
![calculus - why $\int_{-\infty}^{\infty} \left\vert e^{-ax} \right\vert^{2} dx = \int_{0}^{\infty} e^{-2ax}dx$ - Mathematics Stack Exchange calculus - why $\int_{-\infty}^{\infty} \left\vert e^{-ax} \right\vert^{2} dx = \int_{0}^{\infty} e^{-2ax}dx$ - Mathematics Stack Exchange](https://i.stack.imgur.com/zEiIP.png)