Sr Examen

Otras calculadoras

Resolución de integrales/ sin^3/ xcosx/ (sin^3)xcosx

Integral de (sin^3)xcosx dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                    
  /                    
 |                     
 |     3               
 |  sin (x)*x*cos(x) dx
 |                     
/                      
0
∫01xsin⁡3(x)cos⁡(x) dx\int\limits_{0}^{1} x \sin^{3}{\left(x \right)} \cos{\left(x \right)}\, dx 
Integral((sin(x)^3*x)*cos(x), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                               
 |                                  4           3                    4           3                    2       2   
 |    3                      3*x*cos (x)   3*cos (x)*sin(x)   5*x*sin (x)   5*sin (x)*cos(x)   3*x*cos (x)*sin (x)
 | sin (x)*x*cos(x) dx = C - ----------- + ---------------- + ----------- + ---------------- - -------------------
 |                                32              32               32              32                   16        
/
∫xsin⁡3(x)cos⁡(x) dx=C+5xsin⁡4(x)32−3xsin⁡2(x)cos⁡2(x)16−3xcos⁡4(x)32+5sin⁡3(x)cos⁡(x)32+3sin⁡(x)cos⁡3(x)32\int x \sin^{3}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{5 x \sin^{4}{\left(x \right)}}{32} - \frac{3 x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{16} - \frac{3 x \cos^{4}{\left(x \right)}}{32} + \frac{5 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{32} + \frac{3 \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{32}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.00.5
Trazar el gráfico f(x)
Respuesta [src] 
       4           4           2       2           3                  3          
  3*cos (1)   5*sin (1)   3*cos (1)*sin (1)   3*cos (1)*sin(1)   5*sin (1)*cos(1)
- --------- + --------- - ----------------- + ---------------- + ----------------
      32          32              16                 32                 32
−3sin⁡2(1)cos⁡2(1)16−3cos⁡4(1)32+3sin⁡(1)cos⁡3(1)32+5sin⁡3(1)cos⁡(1)32+5sin⁡4(1)32- \frac{3 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{16} - \frac{3 \cos^{4}{\left(1 \right)}}{32} + \frac{3 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{32} + \frac{5 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{32} + \frac{5 \sin^{4}{\left(1 \right)}}{32} 
=
= 
       4           4           2       2           3                  3          
  3*cos (1)   5*sin (1)   3*cos (1)*sin (1)   3*cos (1)*sin(1)   5*sin (1)*cos(1)
- --------- + --------- - ----------------- + ---------------- + ----------------
      32          32              16                 32                 32
−3sin⁡2(1)cos⁡2(1)16−3cos⁡4(1)32+3sin⁡(1)cos⁡3(1)32+5sin⁡3(1)cos⁡(1)32+5sin⁡4(1)32- \frac{3 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{16} - \frac{3 \cos^{4}{\left(1 \right)}}{32} + \frac{3 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{32} + \frac{5 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{32} + \frac{5 \sin^{4}{\left(1 \right)}}{32} 
-3*cos(1)^4/32 + 5*sin(1)^4/32 - 3*cos(1)^2*sin(1)^2/16 + 3*cos(1)^3*sin(1)/32 + 5*sin(1)^3*cos(1)/32
Respuesta numérica [src] 
0.0943356000876032
0.0943356000876032

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

    © Sr Examen – Калькулятор