Sr Examen
Integral de sin(x/3)*sin(3x/2) dx
Solución
Ha introducido
[src]
pi -- 4 / | | /x\ /3*x\ | sin|-|*sin|---| dx | \3/ \ 2 / | / 0
$$\int\limits_{0}^{\frac{\pi}{4}} \sin{\left(\frac{3 x}{2} \right)} \sin{\left(\frac{x}{3} \right)}\, dx$$
Integral(sin(x/3)*sin((3*x)/2), (x, 0, pi/4))
Respuesta (Indefinida)
[src]
/ /11*x\ /7*x\ | 3*sin|----| 3*sin|---| | /x\ /3*x\ \ 6 / \ 6 / | sin|-|*sin|---| dx = C - ----------- + ---------- | \3/ \ 2 / 11 7 | /
$$\int \sin{\left(\frac{3 x}{2} \right)} \sin{\left(\frac{x}{3} \right)}\, dx = C + \frac{3 \sin{\left(\frac{7 x}{6} \right)}}{7} - \frac{3 \sin{\left(\frac{11 x}{6} \right)}}{11}$$
Gráfica
Respuesta
[src]
___________ ___________
/ ___ / ___ ___\ / ___ / ___ ___\
/ 1 \/ 2 | \/ 2 \/ 6 | / 1 \/ 2 |\/ 2 \/ 6 |
54* / - - ----- *|- ----- + -----| 12* / - + ----- *|----- + -----|
\/ 2 4 \ 4 4 / \/ 2 4 \ 4 4 /
- ------------------------------------- + -----------------------------------
77 77
$$- \frac{54 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}\right)}{77} + \frac{12 \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} \left(\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}\right)}{77}$$
=
=
___________ ___________
/ ___ / ___ ___\ / ___ / ___ ___\
/ 1 \/ 2 | \/ 2 \/ 6 | / 1 \/ 2 |\/ 2 \/ 6 |
54* / - - ----- *|- ----- + -----| 12* / - + ----- *|----- + -----|
\/ 2 4 \ 4 4 / \/ 2 4 \ 4 4 /
- ------------------------------------- + -----------------------------------
77 77
$$- \frac{54 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}\right)}{77} + \frac{12 \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} \left(\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}\right)}{77}$$
-54*sqrt(1/2 - sqrt(2)/4)*(-sqrt(2)/4 + sqrt(6)/4)/77 + 12*sqrt(1/2 + sqrt(2)/4)*(sqrt(2)/4 + sqrt(6)/4)/77
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.