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Resolución de integrales/ sin²2x

Integral de sin²2x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1            
  /            
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 |     22      
 |  sin  (x) dx
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/              
0
∫01sin⁡22(x) dx\int\limits_{0}^{1} \sin^{22}{\left(x \right)}\, dx 
Integral(sin(x)^22, (x, 0, 1))
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.025-0.025
Trazar el gráfico f(x)
Respuesta [src] 
                                        3                      5                      7                     9                     11                     15                    13                    17                   19                21          
88179    88179*cos(1)*sin(1)   29393*sin (1)*cos(1)   29393*sin (1)*cos(1)   12597*sin (1)*cos(1)   4199*sin (1)*cos(1)   4199*sin  (1)*cos(1)   2261*sin  (1)*cos(1)   323*sin  (1)*cos(1)   133*sin  (1)*cos(1)   21*sin  (1)*cos(1)   sin  (1)*cos(1)
------ - ------------------- - -------------------- - -------------------- - -------------------- - ------------------- - -------------------- - -------------------- - ------------------- - ------------------- - ------------------ - ---------------
524288          524288                262144                 327680                 163840                 61440                 67584                  42240                   5632                  2640                 440                  22
−88179sin⁡(1)cos⁡(1)524288−29393sin⁡3(1)cos⁡(1)262144−29393sin⁡5(1)cos⁡(1)327680−12597sin⁡7(1)cos⁡(1)163840−4199sin⁡9(1)cos⁡(1)61440−4199sin⁡11(1)cos⁡(1)67584−323sin⁡13(1)cos⁡(1)5632−2261sin⁡15(1)cos⁡(1)42240−133sin⁡17(1)cos⁡(1)2640−21sin⁡19(1)cos⁡(1)440−sin⁡21(1)cos⁡(1)22+88179524288- \frac{88179 \sin{\left(1 \right)} \cos{\left(1 \right)}}{524288} - \frac{29393 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{262144} - \frac{29393 \sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{327680} - \frac{12597 \sin^{7}{\left(1 \right)} \cos{\left(1 \right)}}{163840} - \frac{4199 \sin^{9}{\left(1 \right)} \cos{\left(1 \right)}}{61440} - \frac{4199 \sin^{11}{\left(1 \right)} \cos{\left(1 \right)}}{67584} - \frac{323 \sin^{13}{\left(1 \right)} \cos{\left(1 \right)}}{5632} - \frac{2261 \sin^{15}{\left(1 \right)} \cos{\left(1 \right)}}{42240} - \frac{133 \sin^{17}{\left(1 \right)} \cos{\left(1 \right)}}{2640} - \frac{21 \sin^{19}{\left(1 \right)} \cos{\left(1 \right)}}{440} - \frac{\sin^{21}{\left(1 \right)} \cos{\left(1 \right)}}{22} + \frac{88179}{524288} 
=
= 
                                        3                      5                      7                     9                     11                     15                    13                    17                   19                21          
88179    88179*cos(1)*sin(1)   29393*sin (1)*cos(1)   29393*sin (1)*cos(1)   12597*sin (1)*cos(1)   4199*sin (1)*cos(1)   4199*sin  (1)*cos(1)   2261*sin  (1)*cos(1)   323*sin  (1)*cos(1)   133*sin  (1)*cos(1)   21*sin  (1)*cos(1)   sin  (1)*cos(1)
------ - ------------------- - -------------------- - -------------------- - -------------------- - ------------------- - -------------------- - -------------------- - ------------------- - ------------------- - ------------------ - ---------------
524288          524288                262144                 327680                 163840                 61440                 67584                  42240                   5632                  2640                 440                  22
−88179sin⁡(1)cos⁡(1)524288−29393sin⁡3(1)cos⁡(1)262144−29393sin⁡5(1)cos⁡(1)327680−12597sin⁡7(1)cos⁡(1)163840−4199sin⁡9(1)cos⁡(1)61440−4199sin⁡11(1)cos⁡(1)67584−323sin⁡13(1)cos⁡(1)5632−2261sin⁡15(1)cos⁡(1)42240−133sin⁡17(1)cos⁡(1)2640−21sin⁡19(1)cos⁡(1)440−sin⁡21(1)cos⁡(1)22+88179524288- \frac{88179 \sin{\left(1 \right)} \cos{\left(1 \right)}}{524288} - \frac{29393 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{262144} - \frac{29393 \sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{327680} - \frac{12597 \sin^{7}{\left(1 \right)} \cos{\left(1 \right)}}{163840} - \frac{4199 \sin^{9}{\left(1 \right)} \cos{\left(1 \right)}}{61440} - \frac{4199 \sin^{11}{\left(1 \right)} \cos{\left(1 \right)}}{67584} - \frac{323 \sin^{13}{\left(1 \right)} \cos{\left(1 \right)}}{5632} - \frac{2261 \sin^{15}{\left(1 \right)} \cos{\left(1 \right)}}{42240} - \frac{133 \sin^{17}{\left(1 \right)} \cos{\left(1 \right)}}{2640} - \frac{21 \sin^{19}{\left(1 \right)} \cos{\left(1 \right)}}{440} - \frac{\sin^{21}{\left(1 \right)} \cos{\left(1 \right)}}{22} + \frac{88179}{524288} 
88179/524288 - 88179*cos(1)*sin(1)/524288 - 29393*sin(1)^3*cos(1)/262144 - 29393*sin(1)^5*cos(1)/327680 - 12597*sin(1)^7*cos(1)/163840 - 4199*sin(1)^9*cos(1)/61440 - 4199*sin(1)^11*cos(1)/67584 - 2261*sin(1)^15*cos(1)/42240 - 323*sin(1)^13*cos(1)/5632 - 133*sin(1)^17*cos(1)/2640 - 21*sin(1)^19*cos(1)/440 - sin(1)^21*cos(1)/22
Respuesta numérica [src] 
0.00140026882208537
0.00140026882208537

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

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