Sr Examen
Integral de (3(x-sinx))²(3(1-cosx))+3(x-sinx)(3(1-cosx))² dx
Solución
Ha introducido
[src]
pi / | | / 2 2\ | \(3*(x - sin(x))) *3*(1 - cos(x)) + 3*(x - sin(x))*(3*(1 - cos(x))) / dx | / 2
$$\int\limits_{2}^{\pi} \left(\left(3 \left(1 - \cos{\left(x \right)}\right)\right)^{2} \cdot 3 \left(x - \sin{\left(x \right)}\right) + \left(3 \left(x - \sin{\left(x \right)}\right)\right)^{2} \cdot 3 \left(1 - \cos{\left(x \right)}\right)\right)\, dx$$
Integral((3*(x - sin(x)))^2*(3*(1 - cos(x))) + (3*(x - sin(x)))*(3*(1 - cos(x)))^2, (x, 2, pi))
Respuesta (Indefinida)
[src]
/ | 2 2 2 2 2 2 | / 2 2\ 2 3 3 27*sin (x) 27*x 27*x *cos (x) 27*x *sin (x) 27*x*cos(x)*sin(x) | \(3*(x - sin(x))) *3*(1 - cos(x)) + 3*(x - sin(x))*(3*(1 - cos(x))) / dx = C - 27*cos (x) - 27*cos(x) + 9*(x - sin(x)) + 9*cos (x) - ---------- + ----- - 54*x*sin(x) + ------------- + ------------- + ------------------ | 4 2 4 4 2 /
$$\int \left(\left(3 \left(1 - \cos{\left(x \right)}\right)\right)^{2} \cdot 3 \left(x - \sin{\left(x \right)}\right) + \left(3 \left(x - \sin{\left(x \right)}\right)\right)^{2} \cdot 3 \left(1 - \cos{\left(x \right)}\right)\right)\, dx = C + \frac{27 x^{2} \sin^{2}{\left(x \right)}}{4} + \frac{27 x^{2} \cos^{2}{\left(x \right)}}{4} + \frac{27 x^{2}}{2} + \frac{27 x \sin{\left(x \right)} \cos{\left(x \right)}}{2} - 54 x \sin{\left(x \right)} + 9 \left(x - \sin{\left(x \right)}\right)^{3} - \frac{27 \sin^{2}{\left(x \right)}}{4} + 9 \cos^{3}{\left(x \right)} - 27 \cos^{2}{\left(x \right)} - 27 \cos{\left(x \right)}$$
Gráfica
Respuesta
[src]
2 2 513 2 3 3 3 27*cos (2) 81*pi - --- - 81*sin (2) - 9*cos (2) + 9*pi + 9*sin (2) + 27*cos(2) + 216*sin(2) - ---------- + ------ - 27*cos(2)*sin(2) 4 4 4
$$- \frac{513}{4} - 81 \sin^{2}{\left(2 \right)} + 27 \cos{\left(2 \right)} - \frac{27 \cos^{2}{\left(2 \right)}}{4} - 9 \cos^{3}{\left(2 \right)} + 9 \sin^{3}{\left(2 \right)} - 27 \sin{\left(2 \right)} \cos{\left(2 \right)} + 216 \sin{\left(2 \right)} + \frac{81 \pi^{2}}{4} + 9 \pi^{3}$$
=
=
2 2 513 2 3 3 3 27*cos (2) 81*pi - --- - 81*sin (2) - 9*cos (2) + 9*pi + 9*sin (2) + 27*cos(2) + 216*sin(2) - ---------- + ------ - 27*cos(2)*sin(2) 4 4 4
$$- \frac{513}{4} - 81 \sin^{2}{\left(2 \right)} + 27 \cos{\left(2 \right)} - \frac{27 \cos^{2}{\left(2 \right)}}{4} - 9 \cos^{3}{\left(2 \right)} + 9 \sin^{3}{\left(2 \right)} - 27 \sin{\left(2 \right)} \cos{\left(2 \right)} + 216 \sin{\left(2 \right)} + \frac{81 \pi^{2}}{4} + 9 \pi^{3}$$
-513/4 - 81*sin(2)^2 - 9*cos(2)^3 + 9*pi^3 + 9*sin(2)^3 + 27*cos(2) + 216*sin(2) - 27*cos(2)^2/4 + 81*pi^2/4 - 27*cos(2)*sin(2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.