Sr Examen
Integral de 1/x^2sqrt(9-x^2) dx
Solución
Ha introducido
[src]
sinh(2)
/
|
| ________
| / 2
| \/ 9 - x
| ----------- dx
| 2
| x
|
/
sinh(1)
$$\int\limits_{\sinh{\left(1 \right)}}^{\sinh{\left(2 \right)}} \frac{\sqrt{9 - x^{2}}}{x^{2}}\, dx$$
Integral(sqrt(9 - x^2)/x^2, (x, sinh(1), sinh(2)))
Respuesta (Indefinida)
[src]
/ | | ________ ________ | / 2 / 2 | \/ 9 - x /x\ \/ 9 - x | ----------- dx = C - asin|-| - ----------- | 2 \3/ x | x | /
$$\int \frac{\sqrt{9 - x^{2}}}{x^{2}}\, dx = C - \operatorname{asin}{\left(\frac{x}{3} \right)} - \frac{\sqrt{9 - x^{2}}}{x}$$
Gráfica
Respuesta
[src]
______________ ______________
/ 2 / 2
/sinh(2)\ \/ 9 - sinh (1) \/ 9 - sinh (2) /sinh(1)\
- asin|-------| + ----------------- - ----------------- + asin|-------|
\ 3 / sinh(1) sinh(2) \ 3 /
$$\operatorname{asin}{\left(\frac{\sinh{\left(1 \right)}}{3} \right)} + \frac{\sqrt{9 - \sinh^{2}{\left(1 \right)}}}{\sinh{\left(1 \right)}} - \frac{\sqrt{9 - \sinh^{2}{\left(2 \right)}}}{\sinh{\left(2 \right)}} - \operatorname{asin}{\left(\frac{\sinh{\left(2 \right)}}{3} \right)}$$
=
=
______________ ______________
/ 2 / 2
/sinh(2)\ \/ 9 - sinh (1) \/ 9 - sinh (2) /sinh(1)\
- asin|-------| + ----------------- - ----------------- + asin|-------|
\ 3 / sinh(1) sinh(2) \ 3 /
$$\operatorname{asin}{\left(\frac{\sinh{\left(1 \right)}}{3} \right)} + \frac{\sqrt{9 - \sinh^{2}{\left(1 \right)}}}{\sinh{\left(1 \right)}} - \frac{\sqrt{9 - \sinh^{2}{\left(2 \right)}}}{\sinh{\left(2 \right)}} - \operatorname{asin}{\left(\frac{\sinh{\left(2 \right)}}{3} \right)}$$
-asin(sinh(2)/3) + sqrt(9 - sinh(1)^2)/sinh(1) - sqrt(9 - sinh(2)^2)/sinh(2) + asin(sinh(1)/3)
Respuesta numérica
[src]
(1.18054511925678 + 0.0737457880827969j)
(1.18054511925678 + 0.0737457880827969j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.