Integral de 2\π*x*(π+x)*sin(n*x) dx
Solución
Respuesta (Indefinida)
[src]
// 0 for n = 0\
|| |
|| //cos(n*x) x*sin(n*x) \ | / // 0 for n = 0\ \
|| ||-------- + ---------- for n != 0| | | || | |
|| || 2 n | | | || //sin(n*x) \ | // 0 for n = 0\| // 0 for n = 0\
|| || n | | | || ||-------- for n != 0| | || || 2 || |
- 4*|<-|< | | + 2*pi*|- |<-|< n | | + x*|<-cos(n*x) || + 2*x *|<-cos(n*x) |
|| || 2 | | | || || | | ||---------- otherwise|| ||---------- otherwise|
|| || x | | | || \\ x otherwise / | \\ n /| \\ n /
|| || -- otherwise | | | ||------------------------- otherwise| |
/ || \\ 2 / | \ \\ n / /
| ||-------------------------------------- otherwise|
| 2 \\ n /
| --*x*(pi + x)*sin(n*x) dx = C + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| pi pi
|
/
∫π2x(x+π)sin(nx)dx=C+π2x2({0−ncos(nx)forn=0otherwise)+2πx({0−ncos(nx)forn=0otherwise)−⎩⎨⎧0−n{nsin(nx)xforn=0otherwiseforn=0otherwise−4⎩⎨⎧0−n{nxsin(nx)+n2cos(nx)2x2forn=0otherwiseforn=0otherwise
/ /2*cos(pi*n) pi*sin(pi*n)\
| 2*|----------- + ------------|
| | 3 2 |
| \ n n / 4
<- ------------------------------ + ----- for And(n > -oo, n < oo, n != 0)
| pi 3
| pi*n
|
\ 0 otherwise
{−π2(n2πsin(πn)+n32cos(πn))+πn340forn>−∞∧n<∞∧n=0otherwise
=
/ /2*cos(pi*n) pi*sin(pi*n)\
| 2*|----------- + ------------|
| | 3 2 |
| \ n n / 4
<- ------------------------------ + ----- for And(n > -oo, n < oo, n != 0)
| pi 3
| pi*n
|
\ 0 otherwise
{−π2(n2πsin(πn)+n32cos(πn))+πn340forn>−∞∧n<∞∧n=0otherwise
Piecewise((-2*(2*cos(pi*n)/n^3 + pi*sin(pi*n)/n^2)/pi + 4/(pi*n^3), (n > -oo)∧(n < oo)∧(Ne(n, 0))), (0, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.