Sr Examen

Otras calculadoras

Resolución de integrales/ cos^6/ (144)(cos^6)*3x

Integral de (144)(cos^6)*3x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                   
  /                   
 |                    
 |         6          
 |  144*cos (x)*3*x dx
 |                    
/                     
0
∫01x3⋅144cos⁡6(x) dx\int\limits_{0}^{1} x 3 \cdot 144 \cos^{6}{\left(x \right)}\, dx 
Integral(((144*cos(x)^6)*3)*x, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                                
 |                                 6            6                                2    6           2    6                                                                                 2    2       4           2    4       2   
 |        6                 105*sin (x)   99*cos (x)         2       4      135*x *cos (x)   135*x *sin (x)            5                      5                      3       3      405*x *cos (x)*sin (x)   405*x *cos (x)*sin (x)
 | 144*cos (x)*3*x dx = C - ----------- + ---------- - 90*cos (x)*sin (x) + -------------- + -------------- + 135*x*sin (x)*cos(x) + 297*x*cos (x)*sin(x) + 360*x*cos (x)*sin (x) + ---------------------- + ----------------------
 |                               2            2                                   2                2                                                                                          2                        2           
/
∫x3⋅144cos⁡6(x) dx=C+135x2sin⁡6(x)2+405x2sin⁡4(x)cos⁡2(x)2+405x2sin⁡2(x)cos⁡4(x)2+135x2cos⁡6(x)2+135xsin⁡5(x)cos⁡(x)+360xsin⁡3(x)cos⁡3(x)+297xsin⁡(x)cos⁡5(x)−105sin⁡6(x)2−90sin⁡4(x)cos⁡2(x)+99cos⁡6(x)2\int x 3 \cdot 144 \cos^{6}{\left(x \right)}\, dx = C + \frac{135 x^{2} \sin^{6}{\left(x \right)}}{2} + \frac{405 x^{2} \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{2} + \frac{405 x^{2} \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{2} + \frac{135 x^{2} \cos^{6}{\left(x \right)}}{2} + 135 x \sin^{5}{\left(x \right)} \cos{\left(x \right)} + 360 x \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)} + 297 x \sin{\left(x \right)} \cos^{5}{\left(x \right)} - \frac{105 \sin^{6}{\left(x \right)}}{2} - 90 \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{99 \cos^{6}{\left(x \right)}}{2}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900200
Trazar el gráfico f(x)
Respuesta [src] 
                                                                                                         2       4             4       2   
  99         6             6             5                    5                    3       3      225*cos (1)*sin (1)   405*cos (1)*sin (1)
- -- + 15*sin (1) + 117*cos (1) + 135*sin (1)*cos(1) + 297*cos (1)*sin(1) + 360*cos (1)*sin (1) + ------------------- + -------------------
  2                                                                                                        2                     2
−992+117cos⁡6(1)+15sin⁡6(1)+297sin⁡(1)cos⁡5(1)+405sin⁡2(1)cos⁡4(1)2+225sin⁡4(1)cos⁡2(1)2+135sin⁡5(1)cos⁡(1)+360sin⁡3(1)cos⁡3(1)- \frac{99}{2} + 117 \cos^{6}{\left(1 \right)} + 15 \sin^{6}{\left(1 \right)} + 297 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} + \frac{405 \sin^{2}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{2} + \frac{225 \sin^{4}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{2} + 135 \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} + 360 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} 
=
= 
                                                                                                         2       4             4       2   
  99         6             6             5                    5                    3       3      225*cos (1)*sin (1)   405*cos (1)*sin (1)
- -- + 15*sin (1) + 117*cos (1) + 135*sin (1)*cos(1) + 297*cos (1)*sin(1) + 360*cos (1)*sin (1) + ------------------- + -------------------
  2                                                                                                        2                     2
−992+117cos⁡6(1)+15sin⁡6(1)+297sin⁡(1)cos⁡5(1)+405sin⁡2(1)cos⁡4(1)2+225sin⁡4(1)cos⁡2(1)2+135sin⁡5(1)cos⁡(1)+360sin⁡3(1)cos⁡3(1)- \frac{99}{2} + 117 \cos^{6}{\left(1 \right)} + 15 \sin^{6}{\left(1 \right)} + 297 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} + \frac{405 \sin^{2}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{2} + \frac{225 \sin^{4}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{2} + 135 \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} + 360 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} 
-99/2 + 15*sin(1)^6 + 117*cos(1)^6 + 135*sin(1)^5*cos(1) + 297*cos(1)^5*sin(1) + 360*cos(1)^3*sin(1)^3 + 225*cos(1)^2*sin(1)^4/2 + 405*cos(1)^4*sin(1)^2/2
Respuesta numérica [src] 
63.5334884918399
63.5334884918399

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

    © Sr Examen – Калькулятор