Sr Examen
Integral de cos(3x)*sin(x/4) dx
Solución
Ha introducido
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1 / | | /x\ | cos(3*x)*sin|-| dx | \4/ | / 0
$$\int\limits_{0}^{1} \sin{\left(\frac{x}{4} \right)} \cos{\left(3 x \right)}\, dx$$
Integral(cos(3*x)*sin(x/4), (x, 0, 1))
Respuesta (Indefinida)
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/ 3 /x\ 3 /x\ /x\ /x\ 2 /x\ 2 /x\ | 3008*sin (x)*sin|-| 512*cos (x)*cos|-| 4*cos(x)*cos|-| 16*sin(x)*sin|-| 752*sin (x)*cos(x)*cos|-| 128*cos (x)*sin(x)*sin|-| | /x\ \4/ \4/ \4/ \4/ \4/ \4/ | cos(3*x)*sin|-| dx = C - ------------------- - ------------------ + --------------- + ---------------- - ------------------------- - ------------------------- | \4/ 2145 2145 15 15 2145 2145 | /
$$\int \sin{\left(\frac{x}{4} \right)} \cos{\left(3 x \right)}\, dx = C - \frac{3008 \sin{\left(\frac{x}{4} \right)} \sin^{3}{\left(x \right)}}{2145} - \frac{128 \sin{\left(\frac{x}{4} \right)} \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{2145} + \frac{16 \sin{\left(\frac{x}{4} \right)} \sin{\left(x \right)}}{15} - \frac{752 \sin^{2}{\left(x \right)} \cos{\left(\frac{x}{4} \right)} \cos{\left(x \right)}}{2145} - \frac{512 \cos{\left(\frac{x}{4} \right)} \cos^{3}{\left(x \right)}}{2145} + \frac{4 \cos{\left(\frac{x}{4} \right)} \cos{\left(x \right)}}{15}$$
Gráfica
Respuesta
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4 4*cos(3)*cos(1/4) 48*sin(3)*sin(1/4) - --- + ----------------- + ------------------ 143 143 143
$$- \frac{4}{143} + \frac{4 \cos{\left(\frac{1}{4} \right)} \cos{\left(3 \right)}}{143} + \frac{48 \sin{\left(\frac{1}{4} \right)} \sin{\left(3 \right)}}{143}$$
=
=
4 4*cos(3)*cos(1/4) 48*sin(3)*sin(1/4) - --- + ----------------- + ------------------ 143 143 143
$$- \frac{4}{143} + \frac{4 \cos{\left(\frac{1}{4} \right)} \cos{\left(3 \right)}}{143} + \frac{48 \sin{\left(\frac{1}{4} \right)} \sin{\left(3 \right)}}{143}$$
-4/143 + 4*cos(3)*cos(1/4)/143 + 48*sin(3)*sin(1/4)/143
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.