Sr Examen
Integral de Sin^4(x/3)*cos^2(x/3) dx
Solución
Ha introducido
[src]
1 / | | 4/x\ 2/x\ | sin |-|*cos |-| dx | \3/ \3/ | / 0
$$\int\limits_{0}^{1} \sin^{4}{\left(\frac{x}{3} \right)} \cos^{2}{\left(\frac{x}{3} \right)}\, dx$$
Integral(sin(x/3)^4*cos(x/3)^2, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ 5/x\ /x\ /x\ /x\ 3/x\ /x\ | sin |-|*cos|-| 3*cos|-|*sin|-| sin |-|*cos|-| | 4/x\ 2/x\ x \3/ \3/ \3/ \3/ \3/ \3/ | sin |-|*cos |-| dx = C + -- + -------------- - --------------- - -------------- | \3/ \3/ 16 2 16 8 | /
$$\int \sin^{4}{\left(\frac{x}{3} \right)} \cos^{2}{\left(\frac{x}{3} \right)}\, dx = C + \frac{x}{16} + \frac{\sin^{5}{\left(\frac{x}{3} \right)} \cos{\left(\frac{x}{3} \right)}}{2} - \frac{\sin^{3}{\left(\frac{x}{3} \right)} \cos{\left(\frac{x}{3} \right)}}{8} - \frac{3 \sin{\left(\frac{x}{3} \right)} \cos{\left(\frac{x}{3} \right)}}{16}$$
Gráfica
Respuesta
[src]
5 3 1 sin (1/3)*cos(1/3) 3*cos(1/3)*sin(1/3) sin (1/3)*cos(1/3) -- + ------------------ - ------------------- - ------------------ 16 2 16 8
$$- \frac{3 \sin{\left(\frac{1}{3} \right)} \cos{\left(\frac{1}{3} \right)}}{16} - \frac{\sin^{3}{\left(\frac{1}{3} \right)} \cos{\left(\frac{1}{3} \right)}}{8} + \frac{\sin^{5}{\left(\frac{1}{3} \right)} \cos{\left(\frac{1}{3} \right)}}{2} + \frac{1}{16}$$
=
=
5 3 1 sin (1/3)*cos(1/3) 3*cos(1/3)*sin(1/3) sin (1/3)*cos(1/3) -- + ------------------ - ------------------- - ------------------ 16 2 16 8
$$- \frac{3 \sin{\left(\frac{1}{3} \right)} \cos{\left(\frac{1}{3} \right)}}{16} - \frac{\sin^{3}{\left(\frac{1}{3} \right)} \cos{\left(\frac{1}{3} \right)}}{8} + \frac{\sin^{5}{\left(\frac{1}{3} \right)} \cos{\left(\frac{1}{3} \right)}}{2} + \frac{1}{16}$$
1/16 + sin(1/3)^5*cos(1/3)/2 - 3*cos(1/3)*sin(1/3)/16 - sin(1/3)^3*cos(1/3)/8
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.