Sr Examen
Integral de (sinx-cosx)/(√(1+sin2x)) dx
Solución
Ha introducido
[src]
1 / | | sin(x) - cos(x) | ---------------- dx | ______________ | \/ 1 + sin(2*x) | / 0
$$\int\limits_{0}^{1} \frac{\sin{\left(x \right)} - \cos{\left(x \right)}}{\sqrt{\sin{\left(2 x \right)} + 1}}\, dx$$
Integral((sin(x) - cos(x))/sqrt(1 + sin(2*x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / / | | | | sin(x) - cos(x) | cos(x) | sin(x) | ---------------- dx = C - | ---------------- dx + | ---------------- dx | ______________ | ______________ | ______________ | \/ 1 + sin(2*x) | \/ 1 + sin(2*x) | \/ 1 + sin(2*x) | | | / / /
$$\int \frac{\sin{\left(x \right)} - \cos{\left(x \right)}}{\sqrt{\sin{\left(2 x \right)} + 1}}\, dx = C + \int \frac{\sin{\left(x \right)}}{\sqrt{\sin{\left(2 x \right)} + 1}}\, dx - \int \frac{\cos{\left(x \right)}}{\sqrt{\sin{\left(2 x \right)} + 1}}\, dx$$
Respuesta
[src]
1 1
/ /
| |
| cos(x) | -sin(x)
- | ---------------- dx - | ---------------- dx
| ______________ | ______________
| \/ 1 + sin(2*x) | \/ 1 + sin(2*x)
| |
/ /
0 0
$$- \int\limits_{0}^{1} \frac{\cos{\left(x \right)}}{\sqrt{\sin{\left(2 x \right)} + 1}}\, dx - \int\limits_{0}^{1} \left(- \frac{\sin{\left(x \right)}}{\sqrt{\sin{\left(2 x \right)} + 1}}\right)\, dx$$
=
=
1 1
/ /
| |
| cos(x) | -sin(x)
- | ---------------- dx - | ---------------- dx
| ______________ | ______________
| \/ 1 + sin(2*x) | \/ 1 + sin(2*x)
| |
/ /
0 0
$$- \int\limits_{0}^{1} \frac{\cos{\left(x \right)}}{\sqrt{\sin{\left(2 x \right)} + 1}}\, dx - \int\limits_{0}^{1} \left(- \frac{\sin{\left(x \right)}}{\sqrt{\sin{\left(2 x \right)} + 1}}\right)\, dx$$
-Integral(cos(x)/sqrt(1 + sin(2*x)), (x, 0, 1)) - Integral(-sin(x)/sqrt(1 + sin(2*x)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.