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Resolución de integrales/ sin^4/ (2-x)/ sin^4(2-x)

Integral de sin^4(2-x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1               
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 |  sin (2 - x) dx
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0
∫01sin⁡4(2−x) dx\int\limits_{0}^{1} \sin^{4}{\left(2 - x \right)}\, dx 
Integral(sin(2 - x)^4, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                       3/     x\                                                                  /     x\                                                                                                                                              7/     x\                                                                  5/     x\                                                                   8/     x\                                                                  2/     x\                                                                  6/     x\                                                                  4/     x\                            
 |                                                  22*tan |-1 + -|                                                             6*tan|-1 + -|                                                                                                                                         6*tan |-1 + -|                                                            22*tan |-1 + -|                                                            3*x*tan |-1 + -|                                                          12*x*tan |-1 + -|                                                          12*x*tan |-1 + -|                                                          18*x*tan |-1 + -|                            
 |    4                                                    \     2/                                                                  \     2/                                                                   3*x                                                                         \     2/                                                                   \     2/                                                                    \     2/                                                                   \     2/                                                                   \     2/                                                                   \     2/                            
 | sin (2 - x) dx = C - ------------------------------------------------------------------------ - ------------------------------------------------------------------------ + ------------------------------------------------------------------------ + ------------------------------------------------------------------------ + ------------------------------------------------------------------------ + ------------------------------------------------------------------------ + ------------------------------------------------------------------------ + ------------------------------------------------------------------------ + ------------------------------------------------------------------------
 |                               8/     x\         2/     x\         6/     x\         4/     x\            8/     x\         2/     x\         6/     x\         4/     x\            8/     x\         2/     x\         6/     x\         4/     x\            8/     x\         2/     x\         6/     x\         4/     x\            8/     x\         2/     x\         6/     x\         4/     x\            8/     x\         2/     x\         6/     x\         4/     x\            8/     x\         2/     x\         6/     x\         4/     x\            8/     x\         2/     x\         6/     x\         4/     x\            8/     x\         2/     x\         6/     x\         4/     x\
/                       8 + 8*tan |-1 + -| + 32*tan |-1 + -| + 32*tan |-1 + -| + 48*tan |-1 + -|   8 + 8*tan |-1 + -| + 32*tan |-1 + -| + 32*tan |-1 + -| + 48*tan |-1 + -|   8 + 8*tan |-1 + -| + 32*tan |-1 + -| + 32*tan |-1 + -| + 48*tan |-1 + -|   8 + 8*tan |-1 + -| + 32*tan |-1 + -| + 32*tan |-1 + -| + 48*tan |-1 + -|   8 + 8*tan |-1 + -| + 32*tan |-1 + -| + 32*tan |-1 + -| + 48*tan |-1 + -|   8 + 8*tan |-1 + -| + 32*tan |-1 + -| + 32*tan |-1 + -| + 48*tan |-1 + -|   8 + 8*tan |-1 + -| + 32*tan |-1 + -| + 32*tan |-1 + -| + 48*tan |-1 + -|   8 + 8*tan |-1 + -| + 32*tan |-1 + -| + 32*tan |-1 + -| + 48*tan |-1 + -|   8 + 8*tan |-1 + -| + 32*tan |-1 + -| + 32*tan |-1 + -| + 48*tan |-1 + -|
                                  \     2/          \     2/          \     2/          \     2/             \     2/          \     2/          \     2/          \     2/             \     2/          \     2/          \     2/          \     2/             \     2/          \     2/          \     2/          \     2/             \     2/          \     2/          \     2/          \     2/             \     2/          \     2/          \     2/          \     2/             \     2/          \     2/          \     2/          \     2/             \     2/          \     2/          \     2/          \     2/             \     2/          \     2/          \     2/          \     2/
∫sin⁡4(2−x) dx=C+3xtan⁡8(x2−1)8tan⁡8(x2−1)+32tan⁡6(x2−1)+48tan⁡4(x2−1)+32tan⁡2(x2−1)+8+12xtan⁡6(x2−1)8tan⁡8(x2−1)+32tan⁡6(x2−1)+48tan⁡4(x2−1)+32tan⁡2(x2−1)+8+18xtan⁡4(x2−1)8tan⁡8(x2−1)+32tan⁡6(x2−1)+48tan⁡4(x2−1)+32tan⁡2(x2−1)+8+12xtan⁡2(x2−1)8tan⁡8(x2−1)+32tan⁡6(x2−1)+48tan⁡4(x2−1)+32tan⁡2(x2−1)+8+3x8tan⁡8(x2−1)+32tan⁡6(x2−1)+48tan⁡4(x2−1)+32tan⁡2(x2−1)+8+6tan⁡7(x2−1)8tan⁡8(x2−1)+32tan⁡6(x2−1)+48tan⁡4(x2−1)+32tan⁡2(x2−1)+8+22tan⁡5(x2−1)8tan⁡8(x2−1)+32tan⁡6(x2−1)+48tan⁡4(x2−1)+32tan⁡2(x2−1)+8−22tan⁡3(x2−1)8tan⁡8(x2−1)+32tan⁡6(x2−1)+48tan⁡4(x2−1)+32tan⁡2(x2−1)+8−6tan⁡(x2−1)8tan⁡8(x2−1)+32tan⁡6(x2−1)+48tan⁡4(x2−1)+32tan⁡2(x2−1)+8\int \sin^{4}{\left(2 - x \right)}\, dx = C + \frac{3 x \tan^{8}{\left(\frac{x}{2} - 1 \right)}}{8 \tan^{8}{\left(\frac{x}{2} - 1 \right)} + 32 \tan^{6}{\left(\frac{x}{2} - 1 \right)} + 48 \tan^{4}{\left(\frac{x}{2} - 1 \right)} + 32 \tan^{2}{\left(\frac{x}{2} - 1 \right)} + 8} + \frac{12 x \tan^{6}{\left(\frac{x}{2} - 1 \right)}}{8 \tan^{8}{\left(\frac{x}{2} - 1 \right)} + 32 \tan^{6}{\left(\frac{x}{2} - 1 \right)} + 48 \tan^{4}{\left(\frac{x}{2} - 1 \right)} + 32 \tan^{2}{\left(\frac{x}{2} - 1 \right)} + 8} + \frac{18 x \tan^{4}{\left(\frac{x}{2} - 1 \right)}}{8 \tan^{8}{\left(\frac{x}{2} - 1 \right)} + 32 \tan^{6}{\left(\frac{x}{2} - 1 \right)} + 48 \tan^{4}{\left(\frac{x}{2} - 1 \right)} + 32 \tan^{2}{\left(\frac{x}{2} - 1 \right)} + 8} + \frac{12 x \tan^{2}{\left(\frac{x}{2} - 1 \right)}}{8 \tan^{8}{\left(\frac{x}{2} - 1 \right)} + 32 \tan^{6}{\left(\frac{x}{2} - 1 \right)} + 48 \tan^{4}{\left(\frac{x}{2} - 1 \right)} + 32 \tan^{2}{\left(\frac{x}{2} - 1 \right)} + 8} + \frac{3 x}{8 \tan^{8}{\left(\frac{x}{2} - 1 \right)} + 32 \tan^{6}{\left(\frac{x}{2} - 1 \right)} + 48 \tan^{4}{\left(\frac{x}{2} - 1 \right)} + 32 \tan^{2}{\left(\frac{x}{2} - 1 \right)} + 8} + \frac{6 \tan^{7}{\left(\frac{x}{2} - 1 \right)}}{8 \tan^{8}{\left(\frac{x}{2} - 1 \right)} + 32 \tan^{6}{\left(\frac{x}{2} - 1 \right)} + 48 \tan^{4}{\left(\frac{x}{2} - 1 \right)} + 32 \tan^{2}{\left(\frac{x}{2} - 1 \right)} + 8} + \frac{22 \tan^{5}{\left(\frac{x}{2} - 1 \right)}}{8 \tan^{8}{\left(\frac{x}{2} - 1 \right)} + 32 \tan^{6}{\left(\frac{x}{2} - 1 \right)} + 48 \tan^{4}{\left(\frac{x}{2} - 1 \right)} + 32 \tan^{2}{\left(\frac{x}{2} - 1 \right)} + 8} - \frac{22 \tan^{3}{\left(\frac{x}{2} - 1 \right)}}{8 \tan^{8}{\left(\frac{x}{2} - 1 \right)} + 32 \tan^{6}{\left(\frac{x}{2} - 1 \right)} + 48 \tan^{4}{\left(\frac{x}{2} - 1 \right)} + 32 \tan^{2}{\left(\frac{x}{2} - 1 \right)} + 8} - \frac{6 \tan{\left(\frac{x}{2} - 1 \right)}}{8 \tan^{8}{\left(\frac{x}{2} - 1 \right)} + 32 \tan^{6}{\left(\frac{x}{2} - 1 \right)} + 48 \tan^{4}{\left(\frac{x}{2} - 1 \right)} + 32 \tan^{2}{\left(\frac{x}{2} - 1 \right)} + 8}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.902-1
Trazar el gráfico f(x)
Respuesta [src] 
     4           4           3                  3                  2       2           3                  3          
3*cos (1)   3*sin (1)   5*sin (2)*cos(2)   3*cos (2)*sin(2)   3*cos (1)*sin (1)   3*cos (1)*sin(1)   5*sin (1)*cos(1)
--------- + --------- - ---------------- - ---------------- + ----------------- + ---------------- + ----------------
    8           8              8                  8                   4                  8                  8
−3sin⁡(2)cos⁡3(2)8+3cos⁡4(1)8+3sin⁡(1)cos⁡3(1)8+3sin⁡2(1)cos⁡2(1)4+3sin⁡4(1)8−5sin⁡3(2)cos⁡(2)8+5sin⁡3(1)cos⁡(1)8- \frac{3 \sin{\left(2 \right)} \cos^{3}{\left(2 \right)}}{8} + \frac{3 \cos^{4}{\left(1 \right)}}{8} + \frac{3 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{8} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{4} + \frac{3 \sin^{4}{\left(1 \right)}}{8} - \frac{5 \sin^{3}{\left(2 \right)} \cos{\left(2 \right)}}{8} + \frac{5 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{8} 
=
= 
     4           4           3                  3                  2       2           3                  3          
3*cos (1)   3*sin (1)   5*sin (2)*cos(2)   3*cos (2)*sin(2)   3*cos (1)*sin (1)   3*cos (1)*sin(1)   5*sin (1)*cos(1)
--------- + --------- - ---------------- - ---------------- + ----------------- + ---------------- + ----------------
    8           8              8                  8                   4                  8                  8
−3sin⁡(2)cos⁡3(2)8+3cos⁡4(1)8+3sin⁡(1)cos⁡3(1)8+3sin⁡2(1)cos⁡2(1)4+3sin⁡4(1)8−5sin⁡3(2)cos⁡(2)8+5sin⁡3(1)cos⁡(1)8- \frac{3 \sin{\left(2 \right)} \cos^{3}{\left(2 \right)}}{8} + \frac{3 \cos^{4}{\left(1 \right)}}{8} + \frac{3 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{8} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{4} + \frac{3 \sin^{4}{\left(1 \right)}}{8} - \frac{5 \sin^{3}{\left(2 \right)} \cos{\left(2 \right)}}{8} + \frac{5 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{8} 
3*cos(1)^4/8 + 3*sin(1)^4/8 - 5*sin(2)^3*cos(2)/8 - 3*cos(2)^3*sin(2)/8 + 3*cos(1)^2*sin(1)^2/4 + 3*cos(1)^3*sin(1)/8 + 5*sin(1)^3*cos(1)/8
Respuesta numérica [src] 
0.846092503718756
0.846092503718756

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

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