Sr Examen
Integral de arctg((x/2)^(1/2)) dx
Solución
Ha introducido
[src]
1 / | | / ___\ | | / x | | atan| / - | dx | \\/ 2 / | / 0
$$\int\limits_{0}^{1} \operatorname{atan}{\left(\sqrt{\frac{x}{2}} \right)}\, dx$$
Integral(atan(sqrt(x/2)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / / ___ ___\\ | ___ | ___ ___ |\/ 2 *\/ x || | / ___\ / ___\ \/ 2 *|4*\/ x - 4*\/ 2 *atan|-----------|| | | / x | | / x | \ \ 2 // | atan| / - | dx = C + x*atan| / - | - ------------------------------------------- | \\/ 2 / \\/ 2 / 4 | /
$$\int \operatorname{atan}{\left(\sqrt{\frac{x}{2}} \right)}\, dx = C + x \operatorname{atan}{\left(\sqrt{\frac{x}{2}} \right)} - \frac{\sqrt{2} \left(4 \sqrt{x} - 4 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{x}}{2} \right)}\right)}{4}$$
Gráfica
Respuesta
[src]
/ / ___\\
___ | ___ |\/ 2 ||
\/ 2 *|4 - 4*\/ 2 *atan|-----|| / ___\
\ \ 2 // |\/ 2 |
- ------------------------------- + atan|-----|
4 \ 2 /
$$- \frac{\sqrt{2} \left(- 4 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)} + 4\right)}{4} + \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}$$
=
=
/ / ___\\
___ | ___ |\/ 2 ||
\/ 2 *|4 - 4*\/ 2 *atan|-----|| / ___\
\ \ 2 // |\/ 2 |
- ------------------------------- + atan|-----|
4 \ 2 /
$$- \frac{\sqrt{2} \left(- 4 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)} + 4\right)}{4} + \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}$$
-sqrt(2)*(4 - 4*sqrt(2)*atan(sqrt(2)/2))/4 + atan(sqrt(2)/2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.