Sr Examen
Integral de (sin(2*x-pi/3))^2 dx
Solución
Ha introducido
[src]
pi -- 3 / | | 2/ pi\ | sin |2*x - --| dx | \ 3 / | / 0
$$\int\limits_{0}^{\frac{\pi}{3}} \sin^{2}{\left(2 x - \frac{\pi}{3} \right)}\, dx$$
Integral(sin(2*x - pi/3)^2, (x, 0, pi/3))
Respuesta (Indefinida)
[src]
/ / pi\ 3/ pi\ 4/ pi\ 2/ pi\ | cot|x + --| cot |x + --| x*cot |x + --| 2*x*cot |x + --| | 2/ pi\ x \ 3 / \ 3 / \ 3 / \ 3 / | sin |2*x - --| dx = C + ----------------------------------- + ----------------------------------- - ----------------------------------- + ----------------------------------- + ----------------------------------- | \ 3 / 4/ pi\ 2/ pi\ 4/ pi\ 2/ pi\ 4/ pi\ 2/ pi\ 4/ pi\ 2/ pi\ 4/ pi\ 2/ pi\ | 2 + 2*cot |x + --| + 4*cot |x + --| 2 + 2*cot |x + --| + 4*cot |x + --| 2 + 2*cot |x + --| + 4*cot |x + --| 2 + 2*cot |x + --| + 4*cot |x + --| 2 + 2*cot |x + --| + 4*cot |x + --| / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 /
$$\int \sin^{2}{\left(2 x - \frac{\pi}{3} \right)}\, dx = C + \frac{x \cot^{4}{\left(x + \frac{\pi}{3} \right)}}{2 \cot^{4}{\left(x + \frac{\pi}{3} \right)} + 4 \cot^{2}{\left(x + \frac{\pi}{3} \right)} + 2} + \frac{2 x \cot^{2}{\left(x + \frac{\pi}{3} \right)}}{2 \cot^{4}{\left(x + \frac{\pi}{3} \right)} + 4 \cot^{2}{\left(x + \frac{\pi}{3} \right)} + 2} + \frac{x}{2 \cot^{4}{\left(x + \frac{\pi}{3} \right)} + 4 \cot^{2}{\left(x + \frac{\pi}{3} \right)} + 2} - \frac{\cot^{3}{\left(x + \frac{\pi}{3} \right)}}{2 \cot^{4}{\left(x + \frac{\pi}{3} \right)} + 4 \cot^{2}{\left(x + \frac{\pi}{3} \right)} + 2} + \frac{\cot{\left(x + \frac{\pi}{3} \right)}}{2 \cot^{4}{\left(x + \frac{\pi}{3} \right)} + 4 \cot^{2}{\left(x + \frac{\pi}{3} \right)} + 2}$$
Gráfica
Respuesta
[src]
___
\/ 3 pi
- ----- + --
8 6
$$- \frac{\sqrt{3}}{8} + \frac{\pi}{6}$$
=
=
___
\/ 3 pi
- ----- + --
8 6
$$- \frac{\sqrt{3}}{8} + \frac{\pi}{6}$$
-sqrt(3)/8 + pi/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.