Sr Examen
Integral de sqrt(x^2+y^2-3) dy
Solución
Ha introducido
[src]
1 / | | _____________ | / 2 2 | \/ x + y - 3 dy | / 0
$$\int\limits_{0}^{1} \sqrt{\left(x^{2} + y^{2}\right) - 3}\, dy$$
Integral(sqrt(x^2 + y^2 - 3), (y, 0, 1))
Respuesta (Indefinida)
[src]
_________________________ _________________________
/ 2 / 2
/ y / 2\ / y \ 2 / y / 2\ / y \
/ 3* / 1 + ------------------- *\-3 + x /*asinh|------------------------| x * / 1 + ------------------- *\-3 + x /*asinh|------------------------|
| _____________________ _____________________ _____________________ / / 2\ | _____________________| / / 2\ | _____________________|
| _____________ 3 / / 2\ / / 2\ 2 / / 2\ \/ polar_lift\-3 + x / | / / 2\ | \/ polar_lift\-3 + x / | / / 2\ |
| / 2 2 y *\/ polar_lift\-3 + x / 3*y*\/ polar_lift\-3 + x / y*x *\/ polar_lift\-3 + x / \\/ polar_lift\-3 + x / / \\/ polar_lift\-3 + x / /
| \/ x + y - 3 dy = C + -------------------------------------------------------------------------- - -------------------------------------------------------------------------- + -------------------------------------------------------------------------- - --------------------------------------------------------------------------- + ----------------------------------------------------------------------------
| _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ _________________________
/ / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2
/ y 2 / y / y 2 / y / y 2 / y / y 2 / y / y 2 / y
- 6* / 1 + ------------------- + 2*x * / 1 + ------------------- - 6* / 1 + ------------------- + 2*x * / 1 + ------------------- - 6* / 1 + ------------------- + 2*x * / 1 + ------------------- - 6* / 1 + ------------------- + 2*x * / 1 + ------------------- - 6* / 1 + ------------------- + 2*x * / 1 + -------------------
/ / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\
\/ polar_lift\-3 + x / \/ polar_lift\-3 + x / \/ polar_lift\-3 + x / \/ polar_lift\-3 + x / \/ polar_lift\-3 + x / \/ polar_lift\-3 + x / \/ polar_lift\-3 + x / \/ polar_lift\-3 + x / \/ polar_lift\-3 + x / \/ polar_lift\-3 + x /
$$\int \sqrt{\left(x^{2} + y^{2}\right) - 3}\, dy = C + \frac{x^{2} y \sqrt{\operatorname{polar\_lift}{\left(x^{2} - 3 \right)}}}{2 x^{2} \sqrt{\frac{y^{2}}{\operatorname{polar\_lift}{\left(x^{2} - 3 \right)}} + 1} - 6 \sqrt{\frac{y^{2}}{\operatorname{polar\_lift}{\left(x^{2} - 3 \right)}} + 1}} + \frac{x^{2} \left(x^{2} - 3\right) \sqrt{\frac{y^{2}}{\operatorname{polar\_lift}{\left(x^{2} - 3 \right)}} + 1} \operatorname{asinh}{\left(\frac{y}{\sqrt{\operatorname{polar\_lift}{\left(x^{2} - 3 \right)}}} \right)}}{2 x^{2} \sqrt{\frac{y^{2}}{\operatorname{polar\_lift}{\left(x^{2} - 3 \right)}} + 1} - 6 \sqrt{\frac{y^{2}}{\operatorname{polar\_lift}{\left(x^{2} - 3 \right)}} + 1}} + \frac{y^{3} \sqrt{\operatorname{polar\_lift}{\left(x^{2} - 3 \right)}}}{2 x^{2} \sqrt{\frac{y^{2}}{\operatorname{polar\_lift}{\left(x^{2} - 3 \right)}} + 1} - 6 \sqrt{\frac{y^{2}}{\operatorname{polar\_lift}{\left(x^{2} - 3 \right)}} + 1}} - \frac{3 y \sqrt{\operatorname{polar\_lift}{\left(x^{2} - 3 \right)}}}{2 x^{2} \sqrt{\frac{y^{2}}{\operatorname{polar\_lift}{\left(x^{2} - 3 \right)}} + 1} - 6 \sqrt{\frac{y^{2}}{\operatorname{polar\_lift}{\left(x^{2} - 3 \right)}} + 1}} - \frac{3 \left(x^{2} - 3\right) \sqrt{\frac{y^{2}}{\operatorname{polar\_lift}{\left(x^{2} - 3 \right)}} + 1} \operatorname{asinh}{\left(\frac{y}{\sqrt{\operatorname{polar\_lift}{\left(x^{2} - 3 \right)}}} \right)}}{2 x^{2} \sqrt{\frac{y^{2}}{\operatorname{polar\_lift}{\left(x^{2} - 3 \right)}} + 1} - 6 \sqrt{\frac{y^{2}}{\operatorname{polar\_lift}{\left(x^{2} - 3 \right)}} + 1}}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.