Integral de (2/3(x-1))cos(nx) dx
Solución
Respuesta (Indefinida)
[src]
// 2 \
|| x |
|| -- for n = 0|
|| 2 |
|| |
||/-cos(n*x) |
2*|<|---------- for n != 0 |
||< n |
// x for n = 0\ ||| | // x for n = 0\
|| | ||\ 0 otherwise | || |
/ 2*|
∫ 2 ( x − 1 ) 3 cos ( n x ) d x = C + 2 x ( { x for n = 0 sin ( n x ) n otherwise ) 3 − 2 ( { x for n = 0 sin ( n x ) n otherwise ) 3 − 2 ( { x 2 2 for n = 0 { − cos ( n x ) n for n ≠ 0 0 otherwise n otherwise ) 3 \int \frac{2 \left(x - 1\right)}{3} \cos{\left(n x \right)}\, dx = C + \frac{2 x \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(n x \right)}}{n} & \text{otherwise} \end{cases}\right)}{3} - \frac{2 \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(n x \right)}}{n} & \text{otherwise} \end{cases}\right)}{3} - \frac{2 \left(\begin{cases} \frac{x^{2}}{2} & \text{for}\: n = 0 \\\frac{\begin{cases} - \frac{\cos{\left(n x \right)}}{n} & \text{for}\: n \neq 0 \\0 & \text{otherwise} \end{cases}}{n} & \text{otherwise} \end{cases}\right)}{3} ∫ 3 2 ( x − 1 ) cos ( n x ) d x = C + 3 2 x ( { x n s i n ( n x ) for n = 0 otherwise ) − 3 2 ( { x n s i n ( n x ) for n = 0 otherwise ) − 3 2 ⎩ ⎨ ⎧ 2 x 2 n { − n c o s ( n x ) 0 for n = 0 otherwise for n = 0 otherwise
/-4*sin(4*n)
|----------- for And(n > -oo, n < oo, n != 0)
< 3*n
|
\ -16/3 otherwise
{ − 4 sin ( 4 n ) 3 n for n > − ∞ ∧ n < ∞ ∧ n ≠ 0 − 16 3 otherwise \begin{cases} - \frac{4 \sin{\left(4 n \right)}}{3 n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\- \frac{16}{3} & \text{otherwise} \end{cases} { − 3 n 4 s i n ( 4 n ) − 3 16 for n > − ∞ ∧ n < ∞ ∧ n = 0 otherwise
=
/-4*sin(4*n)
|----------- for And(n > -oo, n < oo, n != 0)
< 3*n
|
\ -16/3 otherwise
{ − 4 sin ( 4 n ) 3 n for n > − ∞ ∧ n < ∞ ∧ n ≠ 0 − 16 3 otherwise \begin{cases} - \frac{4 \sin{\left(4 n \right)}}{3 n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\- \frac{16}{3} & \text{otherwise} \end{cases} { − 3 n 4 s i n ( 4 n ) − 3 16 for n > − ∞ ∧ n < ∞ ∧ n = 0 otherwise
Piecewise((-4*sin(4*n)/(3*n), (n > -oo)∧(n < oo)∧(Ne(n, 0))), (-16/3, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.