Sr Examen
Integral de (7x^2+1)*cos(pi*n*x/2) dx
Solución
Ha introducido
[src]
2 / | | / 2 \ /pi*n*x\ | \7*x + 1/*cos|------| dx | \ 2 / | / 0
$$\int\limits_{0}^{2} \left(7 x^{2} + 1\right) \cos{\left(\frac{x \pi n}{2} \right)}\, dx$$
Integral((7*x^2 + 1)*cos(((pi*n)*x)/2), (x, 0, 2))
Respuesta (Indefinida)
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// 3 \
|| x |
|| -- for n = 0|
|| 3 |
|| |
/ || // /pi*n*x\ /pi*n*x\ \ | // x for n = 0\ // x for n = 0\
| || ||4*sin|------| 2*x*cos|------| | | || | || |
| / 2 \ /pi*n*x\ || || \ 2 / \ 2 / | | 2 || /pi*n*x\ | || /pi*n*x\ |
| \7*x + 1/*cos|------| dx = C - 14*|< ||------------- - --------------- for n != 0| | + 7*x *|<2*sin|------| | + |<2*sin|------| |
| \ 2 / ||2*|< 2 2 pi*n | | || \ 2 / | || \ 2 / |
| || || pi *n | | ||------------- otherwise| ||------------- otherwise|
/ || || | | \\ pi*n / \\ pi*n /
|| || 0 otherwise | |
|| \\ / |
||------------------------------------------------ otherwise|
|| pi*n |
\\ /
$$\int \left(7 x^{2} + 1\right) \cos{\left(\frac{x \pi n}{2} \right)}\, dx = C + 7 x^{2} \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{2 \sin{\left(\frac{\pi n x}{2} \right)}}{\pi n} & \text{otherwise} \end{cases}\right) + \begin{cases} x & \text{for}\: n = 0 \\\frac{2 \sin{\left(\frac{\pi n x}{2} \right)}}{\pi n} & \text{otherwise} \end{cases} - 14 \left(\begin{cases} \frac{x^{3}}{3} & \text{for}\: n = 0 \\\frac{2 \left(\begin{cases} - \frac{2 x \cos{\left(\frac{\pi n x}{2} \right)}}{\pi n} + \frac{4 \sin{\left(\frac{\pi n x}{2} \right)}}{\pi^{2} n^{2}} & \text{for}\: n \neq 0 \\0 & \text{otherwise} \end{cases}\right)}{\pi n} & \text{otherwise} \end{cases}\right)$$
Respuesta
[src]
/ 112*sin(pi*n) 58*sin(pi*n) 112*cos(pi*n) |- ------------- + ------------ + ------------- for And(n > -oo, n < oo, n != 0) | 3 3 pi*n 2 2 < pi *n pi *n | | 62/3 otherwise \
$$\begin{cases} \frac{58 \sin{\left(\pi n \right)}}{\pi n} + \frac{112 \cos{\left(\pi n \right)}}{\pi^{2} n^{2}} - \frac{112 \sin{\left(\pi n \right)}}{\pi^{3} n^{3}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\frac{62}{3} & \text{otherwise} \end{cases}$$
=
=
/ 112*sin(pi*n) 58*sin(pi*n) 112*cos(pi*n) |- ------------- + ------------ + ------------- for And(n > -oo, n < oo, n != 0) | 3 3 pi*n 2 2 < pi *n pi *n | | 62/3 otherwise \
$$\begin{cases} \frac{58 \sin{\left(\pi n \right)}}{\pi n} + \frac{112 \cos{\left(\pi n \right)}}{\pi^{2} n^{2}} - \frac{112 \sin{\left(\pi n \right)}}{\pi^{3} n^{3}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\frac{62}{3} & \text{otherwise} \end{cases}$$
Piecewise((-112*sin(pi*n)/(pi^3*n^3) + 58*sin(pi*n)/(pi*n) + 112*cos(pi*n)/(pi^2*n^2), (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.