Sr Examen
Integral de (2*x+3)*cos(x*K) dx
Solución
Ha introducido
[src]
pi / | | (2*x + 3)*cos(x*k) dx | / -pi
$$\int\limits_{- \pi}^{\pi} \left(2 x + 3\right) \cos{\left(k x \right)}\, dx$$
Integral((2*x + 3)*cos(x*k), (x, -pi, pi))
Respuesta (Indefinida)
[src]
// 2 \
|| x |
|| -- for k = 0|
|| 2 |
/ || | // x for k = 0\ // x for k = 0\
| ||/-cos(k*x) | || | || |
| (2*x + 3)*cos(x*k) dx = C - 2*|<|---------- for k != 0 | + 3*|
$$\int \left(2 x + 3\right) \cos{\left(k x \right)}\, dx = C + 2 x \left(\begin{cases} x & \text{for}\: k = 0 \\\frac{\sin{\left(k x \right)}}{k} & \text{otherwise} \end{cases}\right) + 3 \left(\begin{cases} x & \text{for}\: k = 0 \\\frac{\sin{\left(k x \right)}}{k} & \text{otherwise} \end{cases}\right) - 2 \left(\begin{cases} \frac{x^{2}}{2} & \text{for}\: k = 0 \\\frac{\begin{cases} - \frac{\cos{\left(k x \right)}}{k} & \text{for}\: k \neq 0 \\0 & \text{otherwise} \end{cases}}{k} & \text{otherwise} \end{cases}\right)$$
Respuesta
[src]
/6*sin(pi*k) |----------- for And(k > -oo, k < oo, k != 0) < k | \ 6*pi otherwise
$$\begin{cases} \frac{6 \sin{\left(\pi k \right)}}{k} & \text{for}\: k > -\infty \wedge k < \infty \wedge k \neq 0 \\6 \pi & \text{otherwise} \end{cases}$$
=
=
/6*sin(pi*k) |----------- for And(k > -oo, k < oo, k != 0) < k | \ 6*pi otherwise
$$\begin{cases} \frac{6 \sin{\left(\pi k \right)}}{k} & \text{for}\: k > -\infty \wedge k < \infty \wedge k \neq 0 \\6 \pi & \text{otherwise} \end{cases}$$
Piecewise((6*sin(pi*k)/k, (k > -oo)∧(k < oo)∧(Ne(k, 0))), (6*pi, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.