Sr Examen
Integral de sqrt2xsindx dx
Solución
Ha introducido
[src]
3*pi ---- 2 / | | _____ | \/ 2*x *sin(d)*x dx | / 0
$$\int\limits_{0}^{\frac{3 \pi}{2}} x \sqrt{2 x} \sin{\left(d \right)}\, dx$$
Integral((sqrt(2*x)*sin(d))*x, (x, 0, 3*pi/2))
Respuesta (Indefinida)
[src]
// ___ 5/2 \
/ || 2*\/ 2 *x *sin(d) |
| || ------------------- for |x| < 1|
| _____ || 5 |
| \/ 2*x *sin(d)*x dx = C + |< |
| || ___ __1, 1 / 1 7/2 | \ ___ __0, 2 /7/2, 1 | \ |
/ ||\/ 2 */__ | | x|*sin(d) + \/ 2 */__ | | x|*sin(d) otherwise |
|| \_|2, 2 \5/2 0 | / \_|2, 2 \ 5/2, 0 | / |
\\ /
$$\int x \sqrt{2 x} \sin{\left(d \right)}\, dx = C + \begin{cases} \frac{2 \sqrt{2} x^{\frac{5}{2}} \sin{\left(d \right)}}{5} & \text{for}\: \left|{x}\right| < 1 \\\sqrt{2} {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{7}{2} \\\frac{5}{2} & 0 \end{matrix} \middle| {x} \right)} \sin{\left(d \right)} + \sqrt{2} {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{7}{2}, 1 & \\ & \frac{5}{2}, 0 \end{matrix} \middle| {x} \right)} \sin{\left(d \right)} & \text{otherwise} \end{cases}$$
Respuesta
[src]
___ 5/2
9*\/ 3 *pi *sin(d)
--------------------
10
$$\frac{9 \sqrt{3} \pi^{\frac{5}{2}} \sin{\left(d \right)}}{10}$$
=
=
___ 5/2
9*\/ 3 *pi *sin(d)
--------------------
10
$$\frac{9 \sqrt{3} \pi^{\frac{5}{2}} \sin{\left(d \right)}}{10}$$
9*sqrt(3)*pi^(5/2)*sin(d)/10
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.