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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of sin^2(x)*cos(x)
- Integral of e^x/(1+x)
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Integral of 1/x^6
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Integral of 1/(1-x^2)^1/2
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Identical expressions
- e^(-(one / two)*x²)
- e to the power of ( minus (1 divide by 2) multiply by x²)
- e to the power of ( minus (one divide by two) multiply by x²)
- e(-(1/2)*x²)
- e-1/2*x²
- e^(-(1/2)x²)
- e(-(1/2)x²)
- e-1/2x²
- e^-1/2x²
- e^(-(1 divide by 2)*x²)
- e^(-(1/2)*x²)dx
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Similar expressions
- e^((1/2)*x²)
Integral of e^(-(1/2)*x²) dx
The solution
You have entered
[src]
1 / | | 2 | -x | ---- | 2 | E dx | / 0
$$\int\limits_{0}^{1} e^{- \frac{x^{2}}{2}}\, dx$$
Integral(E^(-x^2/2), (x, 0, 1))
The answer (Indefinite)
[src]
/ | | 2 / ___\ | -x ___ ____ |x*\/ 2 | | ---- \/ 2 *\/ pi *erf|-------| | 2 \ 2 / | E dx = C + ------------------------- | 2 /
$$\int e^{- \frac{x^{2}}{2}}\, dx = C + \frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2}$$
The graph
The answer
[src]
/ ___\
___ ____ |\/ 2 |
\/ 2 *\/ pi *erf|-----|
\ 2 /
-----------------------
2
$$\frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2}}{2} \right)}}{2}$$
=
=
/ ___\
___ ____ |\/ 2 |
\/ 2 *\/ pi *erf|-----|
\ 2 /
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2
$$\frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2}}{2} \right)}}{2}$$
sqrt(2)*sqrt(pi)*erf(sqrt(2)/2)/2
Use the examples entering the upper and lower limits of integration.