Sr Examen
Integral de sqrt((((-a)*sin(2x))^2)+(a*sin(2x))^2) dx
Solución
Ha introducido
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1 / | | ________________________________ | / 2 2 | \/ (-a*sin(2*x)) + (a*sin(2*x)) dx | / 0
$$\int\limits_{0}^{1} \sqrt{\left(- a \sin{\left(2 x \right)}\right)^{2} + \left(a \sin{\left(2 x \right)}\right)^{2}}\, dx$$
Integral(sqrt(((-a)*sin(2*x))^2 + (a*sin(2*x))^2), (x, 0, 1))
Respuesta (Indefinida)
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/
|
| ________________________________ ___ 2
| / 2 2 \/ 2 *a *cos(2*x)*sin(2*x)
| \/ (-a*sin(2*x)) + (a*sin(2*x)) dx = C - --------------------------
| ____ ___________
/ / 2 / 2
2*\/ a *\/ sin (2*x)
$$\int \sqrt{\left(- a \sin{\left(2 x \right)}\right)^{2} + \left(a \sin{\left(2 x \right)}\right)^{2}}\, dx = C - \frac{\sqrt{2} a^{2} \sin{\left(2 x \right)} \cos{\left(2 x \right)}}{2 \sqrt{a^{2}} \sqrt{\sin^{2}{\left(2 x \right)}}}$$
Respuesta
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____ ____
___ / 2 ___ / 2
\/ 2 *\/ a \/ 2 *\/ a *cos(2)
------------- - --------------------
2 2
$$- \frac{\sqrt{2} \sqrt{a^{2}} \cos{\left(2 \right)}}{2} + \frac{\sqrt{2} \sqrt{a^{2}}}{2}$$
=
=
____ ____
___ / 2 ___ / 2
\/ 2 *\/ a \/ 2 *\/ a *cos(2)
------------- - --------------------
2 2
$$- \frac{\sqrt{2} \sqrt{a^{2}} \cos{\left(2 \right)}}{2} + \frac{\sqrt{2} \sqrt{a^{2}}}{2}$$
sqrt(2)*sqrt(a^2)/2 - sqrt(2)*sqrt(a^2)*cos(2)/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.