Sr Examen
Integral de (sin(x/4)^2)*(cos(x/4)^6) dx
Solución
Ha introducido
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1 / | | 2/x\ 6/x\ | sin |-|*cos |-| dx | \4/ \4/ | / 0
$$\int\limits_{0}^{1} \sin^{2}{\left(\frac{x}{4} \right)} \cos^{6}{\left(\frac{x}{4} \right)}\, dx$$
Integral(sin(x/4)^2*cos(x/4)^6, (x, 0, 1))
Respuesta (Indefinida)
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/ 7/x\ /x\ 5/x\ /x\ /x\ /x\ 3/x\ /x\ | cos |-|*sin|-| cos |-|*sin|-| 5*cos|-|*sin|-| 5*cos |-|*sin|-| | 2/x\ 6/x\ 5*x \4/ \4/ \4/ \4/ \4/ \4/ \4/ \4/ | sin |-|*cos |-| dx = C + --- - -------------- + -------------- + --------------- + ---------------- | \4/ \4/ 128 2 12 32 48 | /
$$\int \sin^{2}{\left(\frac{x}{4} \right)} \cos^{6}{\left(\frac{x}{4} \right)}\, dx = C + \frac{5 x}{128} - \frac{\sin{\left(\frac{x}{4} \right)} \cos^{7}{\left(\frac{x}{4} \right)}}{2} + \frac{\sin{\left(\frac{x}{4} \right)} \cos^{5}{\left(\frac{x}{4} \right)}}{12} + \frac{5 \sin{\left(\frac{x}{4} \right)} \cos^{3}{\left(\frac{x}{4} \right)}}{48} + \frac{5 \sin{\left(\frac{x}{4} \right)} \cos{\left(\frac{x}{4} \right)}}{32}$$
Gráfica
Respuesta
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7 5 3 5 cos (1/4)*sin(1/4) cos (1/4)*sin(1/4) 5*cos(1/4)*sin(1/4) 5*cos (1/4)*sin(1/4) --- - ------------------ + ------------------ + ------------------- + -------------------- 128 2 12 32 48
$$- \frac{\sin{\left(\frac{1}{4} \right)} \cos^{7}{\left(\frac{1}{4} \right)}}{2} + \frac{\sin{\left(\frac{1}{4} \right)} \cos^{5}{\left(\frac{1}{4} \right)}}{12} + \frac{5 \sin{\left(\frac{1}{4} \right)} \cos^{3}{\left(\frac{1}{4} \right)}}{48} + \frac{5 \sin{\left(\frac{1}{4} \right)} \cos{\left(\frac{1}{4} \right)}}{32} + \frac{5}{128}$$
=
=
7 5 3 5 cos (1/4)*sin(1/4) cos (1/4)*sin(1/4) 5*cos(1/4)*sin(1/4) 5*cos (1/4)*sin(1/4) --- - ------------------ + ------------------ + ------------------- + -------------------- 128 2 12 32 48
$$- \frac{\sin{\left(\frac{1}{4} \right)} \cos^{7}{\left(\frac{1}{4} \right)}}{2} + \frac{\sin{\left(\frac{1}{4} \right)} \cos^{5}{\left(\frac{1}{4} \right)}}{12} + \frac{5 \sin{\left(\frac{1}{4} \right)} \cos^{3}{\left(\frac{1}{4} \right)}}{48} + \frac{5 \sin{\left(\frac{1}{4} \right)} \cos{\left(\frac{1}{4} \right)}}{32} + \frac{5}{128}$$
5/128 - cos(1/4)^7*sin(1/4)/2 + cos(1/4)^5*sin(1/4)/12 + 5*cos(1/4)*sin(1/4)/32 + 5*cos(1/4)^3*sin(1/4)/48
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.