Sr Examen
Integral de sqrt((4-4cos(x))^2+(4sin(x))^2) dx
Solución
Ha introducido
[src]
2*pi ---- 3 / | | _______________________________ | / 2 2 | \/ (4 - 4*cos(x)) + (4*sin(x)) dx | / pi -- 2
$$\int\limits_{\frac{\pi}{2}}^{\frac{2 \pi}{3}} \sqrt{\left(4 - 4 \cos{\left(x \right)}\right)^{2} + \left(4 \sin{\left(x \right)}\right)^{2}}\, dx$$
Integral(sqrt((4 - 4*cos(x))^2 + (4*sin(x))^2), (x, pi/2, 2*pi/3))
Respuesta (Indefinida)
[src]
/ / | | | _______________________________ | __________________________________ | / 2 2 | / 2 2 | \/ (4 - 4*cos(x)) + (4*sin(x)) dx = C + 4* | \/ 1 + cos (x) + sin (x) - 2*cos(x) dx | | / /
$$\int \sqrt{\left(4 - 4 \cos{\left(x \right)}\right)^{2} + \left(4 \sin{\left(x \right)}\right)^{2}}\, dx = C + 4 \int \sqrt{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} - 2 \cos{\left(x \right)} + 1}\, dx$$
Respuesta
[src]
2*pi
----
3
/
|
| __________________________________
| / 2 2
4* | \/ 1 + cos (x) + sin (x) - 2*cos(x) dx
|
/
pi
--
2
$$4 \int\limits_{\frac{\pi}{2}}^{\frac{2 \pi}{3}} \sqrt{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} - 2 \cos{\left(x \right)} + 1}\, dx$$
=
=
2*pi
----
3
/
|
| __________________________________
| / 2 2
4* | \/ 1 + cos (x) + sin (x) - 2*cos(x) dx
|
/
pi
--
2
$$4 \int\limits_{\frac{\pi}{2}}^{\frac{2 \pi}{3}} \sqrt{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} - 2 \cos{\left(x \right)} + 1}\, dx$$
4*Integral(sqrt(1 + cos(x)^2 + sin(x)^2 - 2*cos(x)), (x, pi/2, 2*pi/3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.