Sr Examen
Integral de cos(20pix-ax) dx
Solución
Ha introducido
[src]
oo / | | cos(20*pi*x - a*x) dx | / 0
$$\int\limits_{0}^{\infty} \cos{\left(- a x + 20 \pi x \right)}\, dx$$
Integral(cos((20*pi)*x - a*x), (x, 0, oo))
Respuesta (Indefinida)
[src]
// sin(a*x - 20*pi*x) \
|| ------------------ for a - 20*pi != 0|
|| a - 20*pi |
|| |
/ ||/ /a*x \ |
| ||| 2*tan|--- - 10*pi*x| |
| cos(20*pi*x - a*x) dx = C + |<| \ 2 / |
| |||------------------------------------------------------------- for a != 20*pi |
/ ||< 2/a*x \ 2/a*x \ otherwise |
|||a - 20*pi + a*tan |--- - 10*pi*x| - 20*pi*tan |--- - 10*pi*x| |
||| \ 2 / \ 2 / |
||| |
\\\ x otherwise /
$$\int \cos{\left(- a x + 20 \pi x \right)}\, dx = C + \begin{cases} \frac{\sin{\left(a x - 20 \pi x \right)}}{a - 20 \pi} & \text{for}\: a - 20 \pi \neq 0 \\\begin{cases} \frac{2 \tan{\left(\frac{a x}{2} - 10 \pi x \right)}}{a \tan^{2}{\left(\frac{a x}{2} - 10 \pi x \right)} + a - 20 \pi \tan^{2}{\left(\frac{a x}{2} - 10 \pi x \right)} - 20 \pi} & \text{for}\: a \neq 20 \pi \\x & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}$$
Respuesta
[src]
/sin(zoo + zoo*a) |---------------- for And(a > -oo, a < oo, a != 20*pi) < a - 20*pi | \ oo otherwise
$$\begin{cases} \frac{\sin{\left(\tilde{\infty} a + \tilde{\infty} \right)}}{a - 20 \pi} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 20 \pi \\\infty & \text{otherwise} \end{cases}$$
=
=
/sin(zoo + zoo*a) |---------------- for And(a > -oo, a < oo, a != 20*pi) < a - 20*pi | \ oo otherwise
$$\begin{cases} \frac{\sin{\left(\tilde{\infty} a + \tilde{\infty} \right)}}{a - 20 \pi} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 20 \pi \\\infty & \text{otherwise} \end{cases}$$
Piecewise((sin(±oo + ±oo*a)/(a - 20*pi), (a > -oo)∧(a < oo)∧(Ne(a, 20*pi))), (oo, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.