Maths calculus

Question

a)π/√2 
B) √π/2
C) π/2 
D)√(π/2

Comments

Take x^2 =t and use Gamma function It will be easiest method

---

Caption

 

Answer 1

On comparing, we get 

                                                               $\int_{-\infty }^{\infty }x^2 e^{-x^2}dx$

                                                              a = 1

answer $ = 1/2\sqrt{\pi /a^3}$

             $=\sqrt{\pi }/2$

These are special integrals, check the link: https://en.wikipedia.org/wiki/List_of_integrals_of_exponential_functions

Comments

any other method ?

---

These all are standard integrals of exponential functions, don't have any other method to solve. I don't have any other method.