Sr Examen
Integral de (7x^2+1)*cos(pi*n*x) dx
Solución
Ha introducido
[src]
2 / | | / 2 \ | \7*x + 1/*cos(pi*n*x) dx | / 0
$$\int\limits_{0}^{2} \left(7 x^{2} + 1\right) \cos{\left(x \pi n \right)}\, dx$$
Integral((7*x^2 + 1)*cos((pi*n)*x), (x, 0, 2))
Respuesta (Indefinida)
[src]
// 3 \
|| x |
|| -- for n = 0|
|| 3 |
/ || |
| ||/sin(pi*n*x) x*cos(pi*n*x) | // x for n = 0\ // x for n = 0\
| / 2 \ |||----------- - ------------- for n != 0 | 2 || | || |
| \7*x + 1/*cos(pi*n*x) dx = C - 14*|<| 2 2 pi*n | + 7*x *|
$$\int \left(7 x^{2} + 1\right) \cos{\left(x \pi n \right)}\, dx = C + 7 x^{2} \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(\pi n x \right)}}{\pi n} & \text{otherwise} \end{cases}\right) + \begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(\pi n x \right)}}{\pi n} & \text{otherwise} \end{cases} - 14 \left(\begin{cases} \frac{x^{3}}{3} & \text{for}\: n = 0 \\\frac{\begin{cases} - \frac{x \cos{\left(\pi n x \right)}}{\pi n} + \frac{\sin{\left(\pi n x \right)}}{\pi^{2} n^{2}} & \text{for}\: n \neq 0 \\0 & \text{otherwise} \end{cases}}{\pi n} & \text{otherwise} \end{cases}\right)$$
Respuesta
[src]
/ 14*sin(2*pi*n) 28*cos(2*pi*n) 29*sin(2*pi*n) |- -------------- + -------------- + -------------- for And(n > -oo, n < oo, n != 0) | 3 3 2 2 pi*n < pi *n pi *n | | 62/3 otherwise \
$$\begin{cases} \frac{29 \sin{\left(2 \pi n \right)}}{\pi n} + \frac{28 \cos{\left(2 \pi n \right)}}{\pi^{2} n^{2}} - \frac{14 \sin{\left(2 \pi n \right)}}{\pi^{3} n^{3}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\frac{62}{3} & \text{otherwise} \end{cases}$$
=
=
/ 14*sin(2*pi*n) 28*cos(2*pi*n) 29*sin(2*pi*n) |- -------------- + -------------- + -------------- for And(n > -oo, n < oo, n != 0) | 3 3 2 2 pi*n < pi *n pi *n | | 62/3 otherwise \
$$\begin{cases} \frac{29 \sin{\left(2 \pi n \right)}}{\pi n} + \frac{28 \cos{\left(2 \pi n \right)}}{\pi^{2} n^{2}} - \frac{14 \sin{\left(2 \pi n \right)}}{\pi^{3} n^{3}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\frac{62}{3} & \text{otherwise} \end{cases}$$
Piecewise((-14*sin(2*pi*n)/(pi^3*n^3) + 28*cos(2*pi*n)/(pi^2*n^2) + 29*sin(2*pi*n)/(pi*n), (n > -oo)∧(n < oo)∧(Ne(n, 0))), (62/3, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.