A calculus problem by Nahom Assefa

Calculus Level 2

∫ e − x 2 d x = ? \large \int e^{-x^2} dx = \ ?

Notation: C C denotes the arbitrary constant of integration .

2 x e x 2 + C 2xe^{x^2}+C e x 2 + C e^{x^2}+C π 2 erfi ( x ) + C \frac {\sqrt \pi}2 \text{erfi }(x)+C 2 e x 2 + C 2e^{x^2}+C

Nahom Assefa by Nahom Assefa , 91, Israel

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Chew-Seong Cheong
Jul 20, 2018

I = ∫ e x 2 d x Since d d z erfi ( z ) = 2 π e z 2 = π 2 erfi ( x ) + C where erfi ( z ) is imaginary error function. \begin{aligned} I & = \int e^{x^2} dx & \small \color{#3D99F6} \text{Since } \frac d{dz} \text{erfi }(z) = \frac 2{\sqrt \pi} e^{z^2} \\ & =\boxed{\dfrac {\sqrt \pi}2 \text{erfi }(x) + C} & \small \color{#3D99F6} \text{where erfi }(z) \text{ is imaginary error function.} \end{aligned}

4 Helpful 0 Interesting 0 Brilliant 0 Confused

so it is the same thing

Nahom Assefa - 2 years, 10 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...