Sr Examen
Integral de ((7-9x^2)^(1/2))/(-9x) dx
Solución
Ha introducido
[src]
1 / | | __________ | / 2 | \/ 7 - 9*x | ------------- dx | -9*x | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{7 - 9 x^{2}}}{\left(-1\right) 9 x}\, dx$$
Integral(sqrt(7 - 9*x^2)/((-9*x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___\ \
|| ___________ ___ |\/ 7 | |
/ || / 2 ___ / 2\ ___ I*\/ 7 *asin|-----| | 2| |
| || I*\/ -7 + 9*x \/ 7 *log\x / \/ 7 *log(x) \ 3*x / 9*|x | |
| __________ ||- ---------------- - ------------- + ------------ - ------------------- for ------ > 1|
| / 2 || 9 18 9 9 7 |
| \/ 7 - 9*x || |
| ------------- dx = C + |< / __________\ |
| -9*x || | / 2 | |
| || __________ ___ | / 9*x | |
/ || / 2 ___ / 2\ \/ 7 *log|1 + / 1 - ---- | |
|| \/ 7 - 9*x \/ 7 *log\x / \ \/ 7 / |
|| - ------------- - ------------- + ------------------------------ otherwise |
|| 9 18 9 |
\\ /
$$\int \frac{\sqrt{7 - 9 x^{2}}}{\left(-1\right) 9 x}\, dx = C + \begin{cases} - \frac{i \sqrt{9 x^{2} - 7}}{9} + \frac{\sqrt{7} \log{\left(x \right)}}{9} - \frac{\sqrt{7} \log{\left(x^{2} \right)}}{18} - \frac{\sqrt{7} i \operatorname{asin}{\left(\frac{\sqrt{7}}{3 x} \right)}}{9} & \text{for}\: \frac{9 \left|{x^{2}}\right|}{7} > 1 \\- \frac{\sqrt{7 - 9 x^{2}}}{9} - \frac{\sqrt{7} \log{\left(x^{2} \right)}}{18} + \frac{\sqrt{7} \log{\left(\sqrt{1 - \frac{9 x^{2}}{7}} + 1 \right)}}{9} & \text{otherwise} \end{cases}$$
Gráfica
Respuesta
[src]
/ ___\
___ |\/ 7 |
___ I*\/ 7 *asin|-----| ___
I*\/ 2 \ 3 / pi*I*\/ 7
-oo - ------- - ------------------- + ----------
9 9 18
$$-\infty - \frac{\sqrt{7} i \operatorname{asin}{\left(\frac{\sqrt{7}}{3} \right)}}{9} - \frac{\sqrt{2} i}{9} + \frac{\sqrt{7} i \pi}{18}$$
=
=
/ ___\
___ |\/ 7 |
___ I*\/ 7 *asin|-----| ___
I*\/ 2 \ 3 / pi*I*\/ 7
-oo - ------- - ------------------- + ----------
9 9 18
$$-\infty - \frac{\sqrt{7} i \operatorname{asin}{\left(\frac{\sqrt{7}}{3} \right)}}{9} - \frac{\sqrt{2} i}{9} + \frac{\sqrt{7} i \pi}{18}$$
-oo - i*sqrt(2)/9 - i*sqrt(7)*asin(sqrt(7)/3)/9 + pi*i*sqrt(7)/18
Respuesta numérica
[src]
(-12.8342347677591 - 0.0128481376576313j)
(-12.8342347677591 - 0.0128481376576313j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.