Sr Examen
Integral de cos^2(П/6-x) dx
Solución
Ha introducido
[src]
pi -- 2 / | | 2/pi \ | cos |-- - x| dx | \6 / | / 6
$$\int\limits_{6}^{\frac{\pi}{2}} \cos^{2}{\left(- x + \frac{\pi}{6} \right)}\, dx$$
Integral(cos(pi/6 - x)^2, (x, 6, pi/2))
Respuesta (Indefinida)
[src]
/ /x 5*pi\ 3/x 5*pi\ 4/x 5*pi\ 2/x 5*pi\ | 2*cot|- + ----| 2*cot |- + ----| x*cot |- + ----| 2*x*cot |- + ----| | 2/pi \ x \2 12 / \2 12 / \2 12 / \2 12 / | cos |-- - x| dx = C + --------------------------------------- - --------------------------------------- + --------------------------------------- + --------------------------------------- + --------------------------------------- | \6 / 4/x 5*pi\ 2/x 5*pi\ 4/x 5*pi\ 2/x 5*pi\ 4/x 5*pi\ 2/x 5*pi\ 4/x 5*pi\ 2/x 5*pi\ 4/x 5*pi\ 2/x 5*pi\ | 2 + 2*cot |- + ----| + 4*cot |- + ----| 2 + 2*cot |- + ----| + 4*cot |- + ----| 2 + 2*cot |- + ----| + 4*cot |- + ----| 2 + 2*cot |- + ----| + 4*cot |- + ----| 2 + 2*cot |- + ----| + 4*cot |- + ----| / \2 12 / \2 12 / \2 12 / \2 12 / \2 12 / \2 12 / \2 12 / \2 12 / \2 12 / \2 12 /
$$\int \cos^{2}{\left(- x + \frac{\pi}{6} \right)}\, dx = C + \frac{x \cot^{4}{\left(\frac{x}{2} + \frac{5 \pi}{12} \right)}}{2 \cot^{4}{\left(\frac{x}{2} + \frac{5 \pi}{12} \right)} + 4 \cot^{2}{\left(\frac{x}{2} + \frac{5 \pi}{12} \right)} + 2} + \frac{2 x \cot^{2}{\left(\frac{x}{2} + \frac{5 \pi}{12} \right)}}{2 \cot^{4}{\left(\frac{x}{2} + \frac{5 \pi}{12} \right)} + 4 \cot^{2}{\left(\frac{x}{2} + \frac{5 \pi}{12} \right)} + 2} + \frac{x}{2 \cot^{4}{\left(\frac{x}{2} + \frac{5 \pi}{12} \right)} + 4 \cot^{2}{\left(\frac{x}{2} + \frac{5 \pi}{12} \right)} + 2} + \frac{2 \cot^{3}{\left(\frac{x}{2} + \frac{5 \pi}{12} \right)}}{2 \cot^{4}{\left(\frac{x}{2} + \frac{5 \pi}{12} \right)} + 4 \cot^{2}{\left(\frac{x}{2} + \frac{5 \pi}{12} \right)} + 2} - \frac{2 \cot{\left(\frac{x}{2} + \frac{5 \pi}{12} \right)}}{2 \cot^{4}{\left(\frac{x}{2} + \frac{5 \pi}{12} \right)} + 4 \cot^{2}{\left(\frac{x}{2} + \frac{5 \pi}{12} \right)} + 2}$$
Gráfica
Respuesta
[src]
/ pi\ / pi\
___ cos|6 + --|*sin|6 + --|
2/ pi\ 2/ pi\ pi \/ 3 \ 3 / \ 3 /
- 3*cos |6 + --| - 3*sin |6 + --| + -- + ----- + -----------------------
\ 3 / \ 3 / 4 8 2
$$- 3 \cos^{2}{\left(\frac{\pi}{3} + 6 \right)} - 3 \sin^{2}{\left(\frac{\pi}{3} + 6 \right)} + \frac{\sqrt{3}}{8} + \frac{\sin{\left(\frac{\pi}{3} + 6 \right)} \cos{\left(\frac{\pi}{3} + 6 \right)}}{2} + \frac{\pi}{4}$$
=
=
/ pi\ / pi\
___ cos|6 + --|*sin|6 + --|
2/ pi\ 2/ pi\ pi \/ 3 \ 3 / \ 3 /
- 3*cos |6 + --| - 3*sin |6 + --| + -- + ----- + -----------------------
\ 3 / \ 3 / 4 8 2
$$- 3 \cos^{2}{\left(\frac{\pi}{3} + 6 \right)} - 3 \sin^{2}{\left(\frac{\pi}{3} + 6 \right)} + \frac{\sqrt{3}}{8} + \frac{\sin{\left(\frac{\pi}{3} + 6 \right)} \cos{\left(\frac{\pi}{3} + 6 \right)}}{2} + \frac{\pi}{4}$$
-3*cos(6 + pi/3)^2 - 3*sin(6 + pi/3)^2 + pi/4 + sqrt(3)/8 + cos(6 + pi/3)*sin(6 + pi/3)/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.