Sr Examen
Integral de tg^2(x/4)*sin^2(x/4) dx
Solución
Ha introducido
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1 / | | 2/x\ 2/x\ | tan |-|*sin |-| dx | \4/ \4/ | / 0
$$\int\limits_{0}^{1} \sin^{2}{\left(\frac{x}{4} \right)} \tan^{2}{\left(\frac{x}{4} \right)}\, dx$$
Integral(tan(x/4)^2*sin(x/4)^2, (x, 0, 1))
Respuesta (Indefinida)
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/ 3/x\ | 4*sin |-| | 2/x\ 2/x\ 3*x \4/ /x\ /x\ | tan |-|*sin |-| dx = C - --- + --------- + 6*cos|-|*sin|-| | \4/ \4/ 2 /x\ \4/ \4/ | cos|-| / \4/
$$\int \sin^{2}{\left(\frac{x}{4} \right)} \tan^{2}{\left(\frac{x}{4} \right)}\, dx = C - \frac{3 x}{2} + \frac{4 \sin^{3}{\left(\frac{x}{4} \right)}}{\cos{\left(\frac{x}{4} \right)}} + 6 \sin{\left(\frac{x}{4} \right)} \cos{\left(\frac{x}{4} \right)}$$
Gráfica
Respuesta
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3 3 4*sin (1/4) - - + ----------- + 6*cos(1/4)*sin(1/4) 2 cos(1/4)
$$- \frac{3}{2} + \frac{4 \sin^{3}{\left(\frac{1}{4} \right)}}{\cos{\left(\frac{1}{4} \right)}} + 6 \sin{\left(\frac{1}{4} \right)} \cos{\left(\frac{1}{4} \right)}$$
=
=
3 3 4*sin (1/4) - - + ----------- + 6*cos(1/4)*sin(1/4) 2 cos(1/4)
$$- \frac{3}{2} + \frac{4 \sin^{3}{\left(\frac{1}{4} \right)}}{\cos{\left(\frac{1}{4} \right)}} + 6 \sin{\left(\frac{1}{4} \right)} \cos{\left(\frac{1}{4} \right)}$$
-3/2 + 4*sin(1/4)^3/cos(1/4) + 6*cos(1/4)*sin(1/4)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.