Let Ι1= displaystyle ∫ 01 ex2 d x and Ι2= displaystyle ∫ 01 2 x2 ex2 d x , then the value of Ι1+Ι2 is equal to

Question

Let Ι1= displaystyle ∫ 01 ex2 d x and Ι2= displaystyle ∫ 01 2 x2 ex2 d x , then the value of Ι1+Ι2 is equal to (A) 1 (B) 2 (C) e (D) e2

Tardigrade Admin · Accepted Answer

Ι2= displaystyle ∫ 01 2 x2 ex2 d x = displaystyle ∫ 01(2 x ex2)xdx Using integration by parts, Ι2=[x ex2]01- displaystyle ∫ 01 ex2 d x Ι2+Ι1=e

Q. Let $I_{1} = \int_{0}^{1} e^{x^{2}} d x$ and $I_{2} = \int_{0}^{1} 2 x^{2} e^{x^{2}} d x$ , then the value of $I_{1} + I_{2}$ is equal to