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