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Resolución de integrales/ cos²2x

Integral de cos²2x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1            
  /            
 |             
 |     22      
 |  cos  (x) dx
 |             
/              
0
∫01cos⁡22(x) dx\int\limits_{0}^{1} \cos^{22}{\left(x \right)}\, dx 
Integral(cos(x)^22, (x, 0, 1))
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9002
Trazar el gráfico f(x)
Respuesta [src] 
            21                   19                    17                    13                     15                     9                     11                      7                      3                      5                                
88179    cos  (1)*sin(1)   21*cos  (1)*sin(1)   133*cos  (1)*sin(1)   323*cos  (1)*sin(1)   2261*cos  (1)*sin(1)   4199*cos (1)*sin(1)   4199*cos  (1)*sin(1)   12597*cos (1)*sin(1)   29393*cos (1)*sin(1)   29393*cos (1)*sin(1)   88179*cos(1)*sin(1)
------ + --------------- + ------------------ + ------------------- + ------------------- + -------------------- + ------------------- + -------------------- + -------------------- + -------------------- + -------------------- + -------------------
524288          22                440                   2640                  5632                 42240                  61440                 67584                  163840                 262144                 327680                 524288
sin⁡(1)cos⁡21(1)22+21sin⁡(1)cos⁡19(1)440+133sin⁡(1)cos⁡17(1)2640+2261sin⁡(1)cos⁡15(1)42240+323sin⁡(1)cos⁡13(1)5632+4199sin⁡(1)cos⁡11(1)67584+4199sin⁡(1)cos⁡9(1)61440+12597sin⁡(1)cos⁡7(1)163840+29393sin⁡(1)cos⁡5(1)327680+29393sin⁡(1)cos⁡3(1)262144+88179sin⁡(1)cos⁡(1)524288+88179524288\frac{\sin{\left(1 \right)} \cos^{21}{\left(1 \right)}}{22} + \frac{21 \sin{\left(1 \right)} \cos^{19}{\left(1 \right)}}{440} + \frac{133 \sin{\left(1 \right)} \cos^{17}{\left(1 \right)}}{2640} + \frac{2261 \sin{\left(1 \right)} \cos^{15}{\left(1 \right)}}{42240} + \frac{323 \sin{\left(1 \right)} \cos^{13}{\left(1 \right)}}{5632} + \frac{4199 \sin{\left(1 \right)} \cos^{11}{\left(1 \right)}}{67584} + \frac{4199 \sin{\left(1 \right)} \cos^{9}{\left(1 \right)}}{61440} + \frac{12597 \sin{\left(1 \right)} \cos^{7}{\left(1 \right)}}{163840} + \frac{29393 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{327680} + \frac{29393 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{262144} + \frac{88179 \sin{\left(1 \right)} \cos{\left(1 \right)}}{524288} + \frac{88179}{524288} 
=
= 
            21                   19                    17                    13                     15                     9                     11                      7                      3                      5                                
88179    cos  (1)*sin(1)   21*cos  (1)*sin(1)   133*cos  (1)*sin(1)   323*cos  (1)*sin(1)   2261*cos  (1)*sin(1)   4199*cos (1)*sin(1)   4199*cos  (1)*sin(1)   12597*cos (1)*sin(1)   29393*cos (1)*sin(1)   29393*cos (1)*sin(1)   88179*cos(1)*sin(1)
------ + --------------- + ------------------ + ------------------- + ------------------- + -------------------- + ------------------- + -------------------- + -------------------- + -------------------- + -------------------- + -------------------
524288          22                440                   2640                  5632                 42240                  61440                 67584                  163840                 262144                 327680                 524288
sin⁡(1)cos⁡21(1)22+21sin⁡(1)cos⁡19(1)440+133sin⁡(1)cos⁡17(1)2640+2261sin⁡(1)cos⁡15(1)42240+323sin⁡(1)cos⁡13(1)5632+4199sin⁡(1)cos⁡11(1)67584+4199sin⁡(1)cos⁡9(1)61440+12597sin⁡(1)cos⁡7(1)163840+29393sin⁡(1)cos⁡5(1)327680+29393sin⁡(1)cos⁡3(1)262144+88179sin⁡(1)cos⁡(1)524288+88179524288\frac{\sin{\left(1 \right)} \cos^{21}{\left(1 \right)}}{22} + \frac{21 \sin{\left(1 \right)} \cos^{19}{\left(1 \right)}}{440} + \frac{133 \sin{\left(1 \right)} \cos^{17}{\left(1 \right)}}{2640} + \frac{2261 \sin{\left(1 \right)} \cos^{15}{\left(1 \right)}}{42240} + \frac{323 \sin{\left(1 \right)} \cos^{13}{\left(1 \right)}}{5632} + \frac{4199 \sin{\left(1 \right)} \cos^{11}{\left(1 \right)}}{67584} + \frac{4199 \sin{\left(1 \right)} \cos^{9}{\left(1 \right)}}{61440} + \frac{12597 \sin{\left(1 \right)} \cos^{7}{\left(1 \right)}}{163840} + \frac{29393 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{327680} + \frac{29393 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{262144} + \frac{88179 \sin{\left(1 \right)} \cos{\left(1 \right)}}{524288} + \frac{88179}{524288} 
88179/524288 + cos(1)^21*sin(1)/22 + 21*cos(1)^19*sin(1)/440 + 133*cos(1)^17*sin(1)/2640 + 323*cos(1)^13*sin(1)/5632 + 2261*cos(1)^15*sin(1)/42240 + 4199*cos(1)^9*sin(1)/61440 + 4199*cos(1)^11*sin(1)/67584 + 12597*cos(1)^7*sin(1)/163840 + 29393*cos(1)^3*sin(1)/262144 + 29393*cos(1)^5*sin(1)/327680 + 88179*cos(1)*sin(1)/524288
Respuesta numérica [src] 
0.264189205926998
0.264189205926998

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

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