Sr Examen
Integral de sqrt(1+(exp^y)^2) dx
Solución
Ha introducido
[src]
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\/ 3
/
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| ___________
| / 2
| / / y\
| \/ 1 + \E / dy
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/
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2*\/ 2
$$\int\limits_{2 \sqrt{2}}^{\sqrt{3}} \sqrt{\left(e^{y}\right)^{2} + 1}\, dy$$
Integral(sqrt(1 + (E^y)^2), (y, 2*sqrt(2), sqrt(3)))
Gráfica
Respuesta
[src]
___ ___ ___ ___
/ ___\ \/ 3 -\/ 3 -2*\/ 2 2*\/ 2 / ___\
| -\/ 3 | e e e e | -2*\/ 2 |
- asinh\e / + ------------------- + ------------------- - ------------------- - ------------------- + asinh\e /
_______________ _______________ _______________ _______________
/ ___ / ___ / ___ / ___
/ -2*\/ 3 / -2*\/ 3 / -4*\/ 2 / -4*\/ 2
\/ 1 + e \/ 1 + e \/ 1 + e \/ 1 + e
$$- \frac{e^{2 \sqrt{2}}}{\sqrt{e^{- 4 \sqrt{2}} + 1}} - \operatorname{asinh}{\left(e^{- \sqrt{3}} \right)} - \frac{1}{\sqrt{e^{- 4 \sqrt{2}} + 1} e^{2 \sqrt{2}}} + \operatorname{asinh}{\left(e^{- 2 \sqrt{2}} \right)} + \frac{1}{\sqrt{e^{- 2 \sqrt{3}} + 1} e^{\sqrt{3}}} + \frac{e^{\sqrt{3}}}{\sqrt{e^{- 2 \sqrt{3}} + 1}}$$
=
=
___ ___ ___ ___
/ ___\ \/ 3 -\/ 3 -2*\/ 2 2*\/ 2 / ___\
| -\/ 3 | e e e e | -2*\/ 2 |
- asinh\e / + ------------------- + ------------------- - ------------------- - ------------------- + asinh\e /
_______________ _______________ _______________ _______________
/ ___ / ___ / ___ / ___
/ -2*\/ 3 / -2*\/ 3 / -4*\/ 2 / -4*\/ 2
\/ 1 + e \/ 1 + e \/ 1 + e \/ 1 + e
$$- \frac{e^{2 \sqrt{2}}}{\sqrt{e^{- 4 \sqrt{2}} + 1}} - \operatorname{asinh}{\left(e^{- \sqrt{3}} \right)} - \frac{1}{\sqrt{e^{- 4 \sqrt{2}} + 1} e^{2 \sqrt{2}}} + \operatorname{asinh}{\left(e^{- 2 \sqrt{2}} \right)} + \frac{1}{\sqrt{e^{- 2 \sqrt{3}} + 1} e^{\sqrt{3}}} + \frac{e^{\sqrt{3}}}{\sqrt{e^{- 2 \sqrt{3}} + 1}}$$
-asinh(exp(-sqrt(3))) + exp(sqrt(3))/sqrt(1 + exp(-2*sqrt(3))) + exp(-sqrt(3))/sqrt(1 + exp(-2*sqrt(3))) - exp(-2*sqrt(2))/sqrt(1 + exp(-4*sqrt(2))) - exp(2*sqrt(2))/sqrt(1 + exp(-4*sqrt(2))) + asinh(exp(-2*sqrt(2)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.