Sr Examen
Integral de sqrt(4-8cosx+4cosx^2+4sinx^2) dx
Solución
Ha introducido
[src]
pi -- 2 / | | ______________________________________ | / 2 2 | \/ 4 - 8*cos(x) + 4*cos (x) + 4*sin (x) dx | / 0
$$\int\limits_{0}^{\frac{\pi}{2}} \sqrt{\left(\left(4 - 8 \cos{\left(x \right)}\right) + 4 \cos^{2}{\left(x \right)}\right) + 4 \sin^{2}{\left(x \right)}}\, dx$$
Integral(sqrt(4 - 8*cos(x) + 4*cos(x)^2 + 4*sin(x)^2), (x, 0, pi/2))
Respuesta (Indefinida)
[src]
/ / | | | ______________________________________ | __________________________________ | / 2 2 | / 2 2 | \/ 4 - 8*cos(x) + 4*cos (x) + 4*sin (x) dx = C + 2* | \/ 1 + cos (x) + sin (x) - 2*cos(x) dx | | / /
$$\int \sqrt{\left(\left(4 - 8 \cos{\left(x \right)}\right) + 4 \cos^{2}{\left(x \right)}\right) + 4 \sin^{2}{\left(x \right)}}\, dx = C + 2 \int \sqrt{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} - 2 \cos{\left(x \right)} + 1}\, dx$$
Respuesta
[src]
pi
--
2
/
|
| __________________________________
| / 2 2
2* | \/ 1 + cos (x) + sin (x) - 2*cos(x) dx
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/
0
$$2 \int\limits_{0}^{\frac{\pi}{2}} \sqrt{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} - 2 \cos{\left(x \right)} + 1}\, dx$$
=
=
pi
--
2
/
|
| __________________________________
| / 2 2
2* | \/ 1 + cos (x) + sin (x) - 2*cos(x) dx
|
/
0
$$2 \int\limits_{0}^{\frac{\pi}{2}} \sqrt{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} - 2 \cos{\left(x \right)} + 1}\, dx$$
2*Integral(sqrt(1 + cos(x)^2 + sin(x)^2 - 2*cos(x)), (x, 0, pi/2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.