$e^{-x^2}$ has no antiderivative in terms of elementary functions (polynomials, exponentials, logarithms, trigonometric functions, etc), but there is a special function defined to fit that role called the error function, $\mathrm{erf}(x)$ , where

$\mathrm{erf}(x)=\displaystyle\frac2{\sqrt\pi}\int_0^xe^{-t^2}\,\mathrm dt$

By the fundamental theorem of calculus, we can see that

$\dfrac{\mathrm d}{\mathrm dx}\mathrm{erf}(x)=\dfrac2{\sqrt\pi}e^{-x^2}$

which means we have

$\displaystyle\int e^{-x^2}\,\mathrm dx=\dfrac{\sqrt\pi}2\mathrm{erf}(x)+C$

8 0

3 years ago

What is the volume of the triangular prism? Enter your answer in the box<br> ___mm^3

luda_lava [24]

Answer:

840mm^3

Step-by-step explanation:

V=(1/2)LWH

L=14

W=10

H=12

14*12*10=1680

Then divide by 2

840

8 0

3 years ago

E=mc

lara [203]

Answer:

Step-by-step explanation:

Divide both sides of the equation by c²

5 0

3 years ago