Sr Examen
Integral de 36*x^4*sin(2*x)*sin(2*x) dx
Solución
Ha introducido
[src]
pi -- 2 / | | 4 | 36*x *sin(2*x)*sin(2*x) dx | / 0
$$\int\limits_{0}^{\frac{\pi}{2}} 36 x^{4} \sin{\left(2 x \right)} \sin{\left(2 x \right)}\, dx$$
Integral(((36*x^4)*sin(2*x))*sin(2*x), (x, 0, pi/2))
Respuesta (Indefinida)
[src]
/ | 2 3 2 3 2 5 2 5 2 2 2 | 4 27*x*sin (2*x) 27*cos(2*x)*sin(2*x) 9*x *cos (2*x) 9*x *sin (2*x) 18*x *cos (2*x) 18*x *sin (2*x) 27*x*cos (2*x) 4 27*x *cos(2*x)*sin(2*x) | 36*x *sin(2*x)*sin(2*x) dx = C - -------------- - -------------------- - -------------- + -------------- + --------------- + --------------- + -------------- - 9*x *cos(2*x)*sin(2*x) + ----------------------- | 16 32 2 2 5 5 16 4 /
$$\int 36 x^{4} \sin{\left(2 x \right)} \sin{\left(2 x \right)}\, dx = C + \frac{18 x^{5} \sin^{2}{\left(2 x \right)}}{5} + \frac{18 x^{5} \cos^{2}{\left(2 x \right)}}{5} - 9 x^{4} \sin{\left(2 x \right)} \cos{\left(2 x \right)} + \frac{9 x^{3} \sin^{2}{\left(2 x \right)}}{2} - \frac{9 x^{3} \cos^{2}{\left(2 x \right)}}{2} + \frac{27 x^{2} \sin{\left(2 x \right)} \cos{\left(2 x \right)}}{4} - \frac{27 x \sin^{2}{\left(2 x \right)}}{16} + \frac{27 x \cos^{2}{\left(2 x \right)}}{16} - \frac{27 \sin{\left(2 x \right)} \cos{\left(2 x \right)}}{32}$$
Gráfica
Respuesta
[src]
3 5
9*pi 9*pi 27*pi
- ----- + ----- + -----
16 80 32
$$- \frac{9 \pi^{3}}{16} + \frac{27 \pi}{32} + \frac{9 \pi^{5}}{80}$$
=
=
3 5
9*pi 9*pi 27*pi
- ----- + ----- + -----
16 80 32
$$- \frac{9 \pi^{3}}{16} + \frac{27 \pi}{32} + \frac{9 \pi^{5}}{80}$$
-9*pi^3/16 + 9*pi^5/80 + 27*pi/32
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.