Sr Examen
Integral de exp(-a*(cos(x))^2)+b*cos(x)*(1+erfc(b*cos(x))) dx
Solución
Ha introducido
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pi -- 2 / | | / 2 \ | | -a*cos (x) | | \e + b*cos(x)*(1 + erfc(b*cos(x)))/ dx | / -pi ---- 2
$$\int\limits_{- \frac{\pi}{2}}^{\frac{\pi}{2}} \left(b \cos{\left(x \right)} \left(\operatorname{erfc}{\left(b \cos{\left(x \right)} \right)} + 1\right) + e^{- a \cos^{2}{\left(x \right)}}\right)\, dx$$
Integral(exp((-a)*cos(x)^2) + (b*cos(x))*(1 + erfc(b*cos(x))), (x, -pi/2, pi/2))
Respuesta (Indefinida)
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/ / | | | / 2 \ / | 2 | | -a*cos (x) | | | -a*cos (x) | \e + b*cos(x)*(1 + erfc(b*cos(x)))/ dx = C + b* | cos(x)*erfc(b*cos(x)) dx + b*sin(x) + | e dx | | | / / /
$$\int \left(b \cos{\left(x \right)} \left(\operatorname{erfc}{\left(b \cos{\left(x \right)} \right)} + 1\right) + e^{- a \cos^{2}{\left(x \right)}}\right)\, dx = C + b \sin{\left(x \right)} + b \int \cos{\left(x \right)} \operatorname{erfc}{\left(b \cos{\left(x \right)} \right)}\, dx + \int e^{- a \cos^{2}{\left(x \right)}}\, dx$$
Respuesta
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pi -- 2 / | | / 2 2 \ 2 | | a*cos (x) a*cos (x)| -a*cos (x) | \1 + b*cos(x)*e + b*cos(x)*erfc(b*cos(x))*e /*e dx | / -pi ---- 2
$$\int\limits_{- \frac{\pi}{2}}^{\frac{\pi}{2}} \left(b e^{a \cos^{2}{\left(x \right)}} \cos{\left(x \right)} \operatorname{erfc}{\left(b \cos{\left(x \right)} \right)} + b e^{a \cos^{2}{\left(x \right)}} \cos{\left(x \right)} + 1\right) e^{- a \cos^{2}{\left(x \right)}}\, dx$$
=
=
pi -- 2 / | | / 2 2 \ 2 | | a*cos (x) a*cos (x)| -a*cos (x) | \1 + b*cos(x)*e + b*cos(x)*erfc(b*cos(x))*e /*e dx | / -pi ---- 2
$$\int\limits_{- \frac{\pi}{2}}^{\frac{\pi}{2}} \left(b e^{a \cos^{2}{\left(x \right)}} \cos{\left(x \right)} \operatorname{erfc}{\left(b \cos{\left(x \right)} \right)} + b e^{a \cos^{2}{\left(x \right)}} \cos{\left(x \right)} + 1\right) e^{- a \cos^{2}{\left(x \right)}}\, dx$$
Integral((1 + b*cos(x)*exp(a*cos(x)^2) + b*cos(x)*erfc(b*cos(x))*exp(a*cos(x)^2))*exp(-a*cos(x)^2), (x, -pi/2, pi/2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.