Sr Examen
Integral de 16√((1-sinx)^2*cosx) dy
Solución
Ha introducido
[src]
pi -- 6 / | | ______________________ | / 2 | 16*\/ (1 - sin(x)) *cos(x) dx | / 0
$$\int\limits_{0}^{\frac{\pi}{6}} 16 \sqrt{\left(1 - \sin{\left(x \right)}\right)^{2} \cos{\left(x \right)}}\, dx$$
Integral(16*sqrt((1 - sin(x))^2*cos(x)), (x, 0, pi/6))
Respuesta
[src]
pi pi
-- --
6 6 0 0
/ / / /
| | | |
| ________ | ________ | ________ | ________
- 16* | -\/ cos(x) dx - 16* | \/ cos(x) *sin(x) dx + 16* | -\/ cos(x) dx + 16* | \/ cos(x) *sin(x) dx
| | | |
/ / / /
$$16 \int\limits^{0} \sin{\left(x \right)} \sqrt{\cos{\left(x \right)}}\, dx - 16 \int\limits^{\frac{\pi}{6}} \sin{\left(x \right)} \sqrt{\cos{\left(x \right)}}\, dx + 16 \int\limits^{0} \left(- \sqrt{\cos{\left(x \right)}}\right)\, dx - 16 \int\limits^{\frac{\pi}{6}} \left(- \sqrt{\cos{\left(x \right)}}\right)\, dx$$
=
=
pi pi
-- --
6 6 0 0
/ / / /
| | | |
| ________ | ________ | ________ | ________
- 16* | -\/ cos(x) dx - 16* | \/ cos(x) *sin(x) dx + 16* | -\/ cos(x) dx + 16* | \/ cos(x) *sin(x) dx
| | | |
/ / / /
$$16 \int\limits^{0} \sin{\left(x \right)} \sqrt{\cos{\left(x \right)}}\, dx - 16 \int\limits^{\frac{\pi}{6}} \sin{\left(x \right)} \sqrt{\cos{\left(x \right)}}\, dx + 16 \int\limits^{0} \left(- \sqrt{\cos{\left(x \right)}}\right)\, dx - 16 \int\limits^{\frac{\pi}{6}} \left(- \sqrt{\cos{\left(x \right)}}\right)\, dx$$
-16*Integral(-sqrt(cos(x)), (x, pi/6)) - 16*Integral(sqrt(cos(x))*sin(x), (x, pi/6)) + 16*Integral(-sqrt(cos(x)), (x, 0)) + 16*Integral(sqrt(cos(x))*sin(x), (x, 0))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.