Sr Examen
Integral de x^2*cos(x*p*k/4) dx
Solución
Ha introducido
[src]
4 / | | 2 /x*p*k\ | x *cos|-----| dx | \ 4 / | / 0
$$\int\limits_{0}^{4} x^{2} \cos{\left(\frac{k p x}{4} \right)}\, dx$$
Integral(x^2*cos(((x*p)*k)/4), (x, 0, 4))
Respuesta (Indefinida)
[src]
// 3 \
|| x |
|| -- for Or(And(k = 0, p = 0), k = 0, p = 0)|
|| 3 |
|| |
/ || // 0 for Or(k = 0, p = 0)\ | // x for Or(k = 0, p = 0)\
| || || | | || |
| 2 /x*p*k\ || || /k*p*x\ /k*p*x\ | | 2 || /k*p*x\ |
| x *cos|-----| dx = C - 2*|< ||16*sin|-----| 4*x*cos|-----| | | + x *|<4*sin|-----| |
| \ 4 / ||4*|< \ 4 / \ 4 / | | || \ 4 / |
| || ||------------- - -------------- otherwise | | ||------------ otherwise |
/ || || 2 2 k*p | | \\ k*p /
|| || k *p | |
|| \\ / |
||--------------------------------------------------------- otherwise |
|| k*p |
\\ /
$$\int x^{2} \cos{\left(\frac{k p x}{4} \right)}\, dx = C + x^{2} \left(\begin{cases} x & \text{for}\: k = 0 \vee p = 0 \\\frac{4 \sin{\left(\frac{k p x}{4} \right)}}{k p} & \text{otherwise} \end{cases}\right) - 2 \left(\begin{cases} \frac{x^{3}}{3} & \text{for}\: \left(k = 0 \wedge p = 0\right) \vee k = 0 \vee p = 0 \\\frac{4 \left(\begin{cases} 0 & \text{for}\: k = 0 \vee p = 0 \\- \frac{4 x \cos{\left(\frac{k p x}{4} \right)}}{k p} + \frac{16 \sin{\left(\frac{k p x}{4} \right)}}{k^{2} p^{2}} & \text{otherwise} \end{cases}\right)}{k p} & \text{otherwise} \end{cases}\right)$$
Respuesta
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/ 64/3 for Or(And(k = 0, p = 0), k = 0, p = 0) | | 128*sin(k*p) 64*sin(k*p) 128*cos(k*p) <- ------------ + ----------- + ------------ otherwise | 3 3 k*p 2 2 | k *p k *p \
$$\begin{cases} \frac{64}{3} & \text{for}\: \left(k = 0 \wedge p = 0\right) \vee k = 0 \vee p = 0 \\\frac{64 \sin{\left(k p \right)}}{k p} + \frac{128 \cos{\left(k p \right)}}{k^{2} p^{2}} - \frac{128 \sin{\left(k p \right)}}{k^{3} p^{3}} & \text{otherwise} \end{cases}$$
=
=
/ 64/3 for Or(And(k = 0, p = 0), k = 0, p = 0) | | 128*sin(k*p) 64*sin(k*p) 128*cos(k*p) <- ------------ + ----------- + ------------ otherwise | 3 3 k*p 2 2 | k *p k *p \
$$\begin{cases} \frac{64}{3} & \text{for}\: \left(k = 0 \wedge p = 0\right) \vee k = 0 \vee p = 0 \\\frac{64 \sin{\left(k p \right)}}{k p} + \frac{128 \cos{\left(k p \right)}}{k^{2} p^{2}} - \frac{128 \sin{\left(k p \right)}}{k^{3} p^{3}} & \text{otherwise} \end{cases}$$
Piecewise((64/3, (k = 0)∨(p = 0)∨((k = 0)∧(p = 0))), (-128*sin(k*p)/(k^3*p^3) + 64*sin(k*p)/(k*p) + 128*cos(k*p)/(k^2*p^2), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.