Sr Examen
Integral de sin^2(x-p/6) dx
Solución
Ha introducido
[src]
p - 3 / | | 2/ p\ | sin |x - -| dx | \ 6/ | / 0
$$\int\limits_{0}^{\frac{p}{3}} \sin^{2}{\left(- \frac{p}{6} + x \right)}\, dx$$
Integral(sin(x - p/6)^2, (x, 0, p/3))
Respuesta (Indefinida)
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/ 3/ x p \ / 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/ | sin |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/
$$\int \sin^{2}{\left(- \frac{p}{6} + x \right)}\, dx = C + \frac{x \tan^{4}{\left(\frac{p}{12} - \frac{x}{2} \right)}}{2 \tan^{4}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 4 \tan^{2}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 2} + \frac{2 x \tan^{2}{\left(\frac{p}{12} - \frac{x}{2} \right)}}{2 \tan^{4}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 4 \tan^{2}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 2} + \frac{x}{2 \tan^{4}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 4 \tan^{2}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 2} - \frac{2 \tan^{3}{\left(\frac{p}{12} - \frac{x}{2} \right)}}{2 \tan^{4}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 4 \tan^{2}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 2} + \frac{2 \tan{\left(\frac{p}{12} - \frac{x}{2} \right)}}{2 \tan^{4}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 4 \tan^{2}{\left(\frac{p}{12} - \frac{x}{2} \right)} + 2}$$
Respuesta
[src]
2/p\ 2/p\
p*cos |-| p*sin |-|
/p\ /p\ \6/ \6/
- cos|-|*sin|-| + --------- + ---------
\6/ \6/ 6 6
$$\frac{p \sin^{2}{\left(\frac{p}{6} \right)}}{6} + \frac{p \cos^{2}{\left(\frac{p}{6} \right)}}{6} - \sin{\left(\frac{p}{6} \right)} \cos{\left(\frac{p}{6} \right)}$$
=
=
2/p\ 2/p\
p*cos |-| p*sin |-|
/p\ /p\ \6/ \6/
- cos|-|*sin|-| + --------- + ---------
\6/ \6/ 6 6
$$\frac{p \sin^{2}{\left(\frac{p}{6} \right)}}{6} + \frac{p \cos^{2}{\left(\frac{p}{6} \right)}}{6} - \sin{\left(\frac{p}{6} \right)} \cos{\left(\frac{p}{6} \right)}$$
-cos(p/6)*sin(p/6) + p*cos(p/6)^2/6 + p*sin(p/6)^2/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.