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