Sr Examen
Integral de -1/(0,1*x^2+(7,4/6)) dx
Solución
Ha introducido
[src]
100 / | | -1 | -------- dx | 2 | x 37 | -- + --- | 10 5*6 | / 14
$$\int\limits_{14}^{100} \left(- \frac{1}{\frac{x^{2}}{10} + \frac{37}{5 \cdot 6}}\right)\, dx$$
Integral(-1/(x^2/10 + 37/(5*6)), (x, 14, 100))
Solución detallada
Tenemos el integral:
/ | | -1 | -------- dx | 2 | x 37 | -- + --- | 10 5*6 | /
Reescribimos la función subintegral
/-1 \
|----|
|/37\|
||--||
-1 \\30//
-------- = ------------------
2 2
x 37 / _____ \
-- + --- |-\/ 111 |
10 5*6 |---------*x| + 1
\ 37 / o
/ | | -1 | -------- dx | 2 | x 37 = | -- + --- | 10 5*6 | /
/
|
| 1
-30* | ------------------ dx
| 2
| / _____ \
| |-\/ 111 |
| |---------*x| + 1
| \ 37 /
|
/
----------------------------
37 En integral
/
|
| 1
-30* | ------------------ dx
| 2
| / _____ \
| |-\/ 111 |
| |---------*x| + 1
| \ 37 /
|
/
----------------------------
37 hacemos el cambio
_____
-x*\/ 111
v = -----------
37 entonces
integral =
/
|
| 1
-30* | ------ dv
| 2
| 1 + v
|
/ -30*atan(v)
---------------- = -----------
37 37 hacemos cambio inverso
/
|
| 1
-30* | ------------------ dx
| 2
| / _____ \
| |-\/ 111 |
| |---------*x| + 1 / _____\
| \ 37 / _____ |x*\/ 111 |
| -10*\/ 111 *atan|---------|
/ \ 37 /
---------------------------- = ---------------------------
37 37 La solución:
/ _____\
_____ |x*\/ 111 |
10*\/ 111 *atan|---------|
\ 37 /
C - --------------------------
37
Respuesta (Indefinida)
[src]
/ _____\ / _____ |x*\/ 111 | | 10*\/ 111 *atan|---------| | -1 \ 37 / | -------- dx = C - -------------------------- | 2 37 | x 37 | -- + --- | 10 5*6 | /
$$\int \left(- \frac{1}{\frac{x^{2}}{10} + \frac{37}{5 \cdot 6}}\right)\, dx = C - \frac{10 \sqrt{111} \operatorname{atan}{\left(\frac{\sqrt{111} x}{37} \right)}}{37}$$
Gráfica
Respuesta
[src]
/ _____\ / _____\
_____ |100*\/ 111 | _____ |14*\/ 111 |
10*\/ 111 *atan|-----------| 10*\/ 111 *atan|----------|
\ 37 / \ 37 /
- ---------------------------- + ---------------------------
37 37
$$- \frac{10 \sqrt{111} \operatorname{atan}{\left(\frac{100 \sqrt{111}}{37} \right)}}{37} + \frac{10 \sqrt{111} \operatorname{atan}{\left(\frac{14 \sqrt{111}}{37} \right)}}{37}$$
=
=
/ _____\ / _____\
_____ |100*\/ 111 | _____ |14*\/ 111 |
10*\/ 111 *atan|-----------| 10*\/ 111 *atan|----------|
\ 37 / \ 37 /
- ---------------------------- + ---------------------------
37 37
$$- \frac{10 \sqrt{111} \operatorname{atan}{\left(\frac{100 \sqrt{111}}{37} \right)}}{37} + \frac{10 \sqrt{111} \operatorname{atan}{\left(\frac{14 \sqrt{111}}{37} \right)}}{37}$$
-10*sqrt(111)*atan(100*sqrt(111)/37)/37 + 10*sqrt(111)*atan(14*sqrt(111)/37)/37
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.