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