Sr Examen

Otras calculadoras

Resolución de integrales/ (x^2)/ sin^4/ cos^4/ xsin^4(x^2)cos^4(x^2)

Integral de xsin^4(x^2)cos^4(x^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                       
  /                       
 |                        
 |       4/ 2\    4/ 2\   
 |  x*sin \x /*cos \x / dx
 |                        
/                         
0
∫01xsin⁡4(x2)cos⁡4(x2) dx\int\limits_{0}^{1} x \sin^{4}{\left(x^{2} \right)} \cos^{4}{\left(x^{2} \right)}\, dx 
Integral((x*sin(x^2)^4)*cos(x^2)^4, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                             
 |                                    5/ 2\    3/ 2\        7/ 2\    / 2\      2    8/ 2\      2    8/ 2\        7/ 2\    / 2\         3/ 2\    5/ 2\      2    2/ 2\    6/ 2\      2    6/ 2\    2/ 2\      2    4/ 2\    4/ 2\
 |      4/ 2\    4/ 2\          11*cos \x /*sin \x /   3*cos \x /*sin\x /   3*x *cos \x /   3*x *sin \x /   3*sin \x /*cos\x /   11*cos \x /*sin \x /   3*x *cos \x /*sin \x /   3*x *cos \x /*sin \x /   9*x *cos \x /*sin \x /
 | x*sin \x /*cos \x / dx = C - -------------------- - ------------------ + ------------- + ------------- + ------------------ + -------------------- + ---------------------- + ---------------------- + ----------------------
 |                                      256                   256                256             256               256                   256                      64                       64                      128          
/
∫xsin⁡4(x2)cos⁡4(x2) dx=C+3x2sin⁡8(x2)256+3x2sin⁡6(x2)cos⁡2(x2)64+9x2sin⁡4(x2)cos⁡4(x2)128+3x2sin⁡2(x2)cos⁡6(x2)64+3x2cos⁡8(x2)256+3sin⁡7(x2)cos⁡(x2)256+11sin⁡5(x2)cos⁡3(x2)256−11sin⁡3(x2)cos⁡5(x2)256−3sin⁡(x2)cos⁡7(x2)256\int x \sin^{4}{\left(x^{2} \right)} \cos^{4}{\left(x^{2} \right)}\, dx = C + \frac{3 x^{2} \sin^{8}{\left(x^{2} \right)}}{256} + \frac{3 x^{2} \sin^{6}{\left(x^{2} \right)} \cos^{2}{\left(x^{2} \right)}}{64} + \frac{9 x^{2} \sin^{4}{\left(x^{2} \right)} \cos^{4}{\left(x^{2} \right)}}{128} + \frac{3 x^{2} \sin^{2}{\left(x^{2} \right)} \cos^{6}{\left(x^{2} \right)}}{64} + \frac{3 x^{2} \cos^{8}{\left(x^{2} \right)}}{256} + \frac{3 \sin^{7}{\left(x^{2} \right)} \cos{\left(x^{2} \right)}}{256} + \frac{11 \sin^{5}{\left(x^{2} \right)} \cos^{3}{\left(x^{2} \right)}}{256} - \frac{11 \sin^{3}{\left(x^{2} \right)} \cos^{5}{\left(x^{2} \right)}}{256} - \frac{3 \sin{\left(x^{2} \right)} \cos^{7}{\left(x^{2} \right)}}{256}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.000.10
Trazar el gráfico f(x)
Respuesta [src] 
     8           8            5       3           7                  2       6           6       2           7                  4       4            3       5   
3*cos (1)   3*sin (1)   11*cos (1)*sin (1)   3*cos (1)*sin(1)   3*cos (1)*sin (1)   3*cos (1)*sin (1)   3*sin (1)*cos(1)   9*cos (1)*sin (1)   11*cos (1)*sin (1)
--------- + --------- - ------------------ - ---------------- + ----------------- + ----------------- + ---------------- + ----------------- + ------------------
   256         256             256                 256                  64                  64                256                 128                 256
−11sin⁡3(1)cos⁡5(1)256−3sin⁡(1)cos⁡7(1)256+3cos⁡8(1)256+3sin⁡2(1)cos⁡6(1)64+3sin⁡7(1)cos⁡(1)256+11sin⁡5(1)cos⁡3(1)256+3sin⁡8(1)256+9sin⁡4(1)cos⁡4(1)128+3sin⁡6(1)cos⁡2(1)64- \frac{11 \sin^{3}{\left(1 \right)} \cos^{5}{\left(1 \right)}}{256} - \frac{3 \sin{\left(1 \right)} \cos^{7}{\left(1 \right)}}{256} + \frac{3 \cos^{8}{\left(1 \right)}}{256} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{6}{\left(1 \right)}}{64} + \frac{3 \sin^{7}{\left(1 \right)} \cos{\left(1 \right)}}{256} + \frac{11 \sin^{5}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{256} + \frac{3 \sin^{8}{\left(1 \right)}}{256} + \frac{9 \sin^{4}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{128} + \frac{3 \sin^{6}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{64} 
=
= 
     8           8            5       3           7                  2       6           6       2           7                  4       4            3       5   
3*cos (1)   3*sin (1)   11*cos (1)*sin (1)   3*cos (1)*sin(1)   3*cos (1)*sin (1)   3*cos (1)*sin (1)   3*sin (1)*cos(1)   9*cos (1)*sin (1)   11*cos (1)*sin (1)
--------- + --------- - ------------------ - ---------------- + ----------------- + ----------------- + ---------------- + ----------------- + ------------------
   256         256             256                 256                  64                  64                256                 128                 256
−11sin⁡3(1)cos⁡5(1)256−3sin⁡(1)cos⁡7(1)256+3cos⁡8(1)256+3sin⁡2(1)cos⁡6(1)64+3sin⁡7(1)cos⁡(1)256+11sin⁡5(1)cos⁡3(1)256+3sin⁡8(1)256+9sin⁡4(1)cos⁡4(1)128+3sin⁡6(1)cos⁡2(1)64- \frac{11 \sin^{3}{\left(1 \right)} \cos^{5}{\left(1 \right)}}{256} - \frac{3 \sin{\left(1 \right)} \cos^{7}{\left(1 \right)}}{256} + \frac{3 \cos^{8}{\left(1 \right)}}{256} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{6}{\left(1 \right)}}{64} + \frac{3 \sin^{7}{\left(1 \right)} \cos{\left(1 \right)}}{256} + \frac{11 \sin^{5}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{256} + \frac{3 \sin^{8}{\left(1 \right)}}{256} + \frac{9 \sin^{4}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{128} + \frac{3 \sin^{6}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{64} 
3*cos(1)^8/256 + 3*sin(1)^8/256 - 11*cos(1)^5*sin(1)^3/256 - 3*cos(1)^7*sin(1)/256 + 3*cos(1)^2*sin(1)^6/64 + 3*cos(1)^6*sin(1)^2/64 + 3*sin(1)^7*cos(1)/256 + 9*cos(1)^4*sin(1)^4/128 + 11*cos(1)^3*sin(1)^5/256
Respuesta numérica [src] 
0.0151580948286557
0.0151580948286557

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

    © Sr Examen – Калькулятор