Integral de (x^2+3)sinnx dx
Solución
Respuesta (Indefinida)
[src]
// 0 for n = 0\
|| |
|| //cos(n*x) x*sin(n*x) \ |
/ || ||-------- + ---------- for n != 0| |
| || || 2 n | | // 0 for n = 0\ // 0 for n = 0\
| / 2 \ || || n | | || | 2 || |
| \x + 3/*sin(n*x) dx = C - 2*|<-|< | | + 3*|<-cos(n*x) | + x *|<-cos(n*x) |
| || || 2 | | ||---------- otherwise| ||---------- otherwise|
/ || || x | | \\ n / \\ n /
|| || -- otherwise | |
|| \\ 2 / |
||-------------------------------------- otherwise|
\\ n /
∫(x2+3)sin(nx)dx=C+x2({0−ncos(nx)forn=0otherwise)−2⎩⎨⎧0−n{nxsin(nx)+n2cos(nx)2x2forn=0otherwiseforn=0otherwise+3({0−ncos(nx)forn=0otherwise)
/ 2
| 2 3 3*cos(2*pi*n) 2*cos(2*pi*n) 4*pi *cos(2*pi*n) 4*pi*sin(2*pi*n)
|- -- + - - ------------- + ------------- - ----------------- + ---------------- for And(n > -oo, n < oo, n != 0)
< 3 n n 3 n 2
| n n n
|
\ 0 otherwise
{−n4π2cos(2πn)−n3cos(2πn)+n3+n24πsin(2πn)+n32cos(2πn)−n320forn>−∞∧n<∞∧n=0otherwise
=
/ 2
| 2 3 3*cos(2*pi*n) 2*cos(2*pi*n) 4*pi *cos(2*pi*n) 4*pi*sin(2*pi*n)
|- -- + - - ------------- + ------------- - ----------------- + ---------------- for And(n > -oo, n < oo, n != 0)
< 3 n n 3 n 2
| n n n
|
\ 0 otherwise
{−n4π2cos(2πn)−n3cos(2πn)+n3+n24πsin(2πn)+n32cos(2πn)−n320forn>−∞∧n<∞∧n=0otherwise
Piecewise((-2/n^3 + 3/n - 3*cos(2*pi*n)/n + 2*cos(2*pi*n)/n^3 - 4*pi^2*cos(2*pi*n)/n + 4*pi*sin(2*pi*n)/n^2, (n > -oo)∧(n < oo)∧(Ne(n, 0))), (0, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.