Sr Examen

Otras calculadoras

Resolución de integrales/ sin(2*x)/ 6*x^4/ 36*x^4*sin(2*x)*sin(2*x)

Integral de 36*x^4*sin(2*x)*sin(2*x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 pi                           
 --                           
 2                            
  /                           
 |                            
 |      4                     
 |  36*x *sin(2*x)*sin(2*x) dx
 |                            
/                             
0
∫0π236x4sin⁡(2x)sin⁡(2x) dx\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           
/
∫36x4sin⁡(2x)sin⁡(2x) dx=C+18x5sin⁡2(2x)5+18x5cos⁡2(2x)5−9x4sin⁡(2x)cos⁡(2x)+9x3sin⁡2(2x)2−9x3cos⁡2(2x)2+27x2sin⁡(2x)cos⁡(2x)4−27xsin⁡2(2x)16+27xcos⁡2(2x)16−27sin⁡(2x)cos⁡(2x)32\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}
Simplificar
Gráfica
0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5050
Trazar el gráfico f(x)
Respuesta [src] 
      3       5        
  9*pi    9*pi    27*pi
- ----- + ----- + -----
    16      80      32
−9π316+27π32+9π580- \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
−9π316+27π32+9π580- \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
Respuesta numérica [src] 
19.6369027071419
19.6369027071419

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

    © Sr Examen – Калькулятор