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- Integral de d{x}:
- sqrt(a^2-x^2)
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Expresiones semejantes
- sqrt(a^2+x^2)
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Expresiones con funciones
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sqrt(a^2-x^2) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
$$\sqrt{a^{2} - x^{2}} = 0$$
cambiamos
$$a^{2} - x^{2} = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = -1$$
$$b = 0$$
$$c = a^{2}$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = - \sqrt{a^{2}}$$
$$x_{2} = \sqrt{a^{2}}$$
cambiamos
$$a^{2} - x^{2} = 0$$
Es la ecuación de la forma
a*x^2 + b*x + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = -1$$
$$b = 0$$
$$c = a^{2}$$
, entonces
D = b^2 - 4 * a * c =
(0)^2 - 4 * (-1) * (a^2) = 4*a^2
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = - \sqrt{a^{2}}$$
$$x_{2} = \sqrt{a^{2}}$$
Gráfica
Respuesta rápida
[src]
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/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/| 4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/|
x1 = - \/ \re (a) - im (a)/ + 4*im (a)*re (a) *cos|-------------------------------------| - I*\/ \re (a) - im (a)/ + 4*im (a)*re (a) *sin|-------------------------------------|
\ 2 / \ 2 /
$$x_{1} = - i \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}$$
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/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/| 4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/|
x2 = \/ \re (a) - im (a)/ + 4*im (a)*re (a) *cos|-------------------------------------| + I*\/ \re (a) - im (a)/ + 4*im (a)*re (a) *sin|-------------------------------------|
\ 2 / \ 2 /
$$x_{2} = i \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}$$
x2 = i*((re(a)^2 - im(a)^2)^2 + 4*re(a)^2*im(a)^2)^(1/4)*sin(atan2(2*re(a)*im(a, re(a)^2 - im(a)^2)/2) + ((re(a)^2 - im(a)^2)^2 + 4*re(a)^2*im(a)^2)^(1/4)*cos(atan2(2*re(a)*im(a), re(a)^2 - im(a)^2)/2))
Suma y producto de raíces
[src]
suma
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/ 2 / / 2 2 \\ / 2 / / 2 2 \\ / 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/| 4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/| 4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/| 4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/|
- \/ \re (a) - im (a)/ + 4*im (a)*re (a) *cos|-------------------------------------| - I*\/ \re (a) - im (a)/ + 4*im (a)*re (a) *sin|-------------------------------------| + \/ \re (a) - im (a)/ + 4*im (a)*re (a) *cos|-------------------------------------| + I*\/ \re (a) - im (a)/ + 4*im (a)*re (a) *sin|-------------------------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
$$\left(- i \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ ______________________________________ ______________________________________ \ / ______________________________________ ______________________________________ \ | / 2 / / 2 2 \\ / 2 / / 2 2 \\| | / 2 / / 2 2 \\ / 2 / / 2 2 \\| | 4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/| 4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/|| |4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/| 4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/|| |- \/ \re (a) - im (a)/ + 4*im (a)*re (a) *cos|-------------------------------------| - I*\/ \re (a) - im (a)/ + 4*im (a)*re (a) *sin|-------------------------------------||*|\/ \re (a) - im (a)/ + 4*im (a)*re (a) *cos|-------------------------------------| + I*\/ \re (a) - im (a)/ + 4*im (a)*re (a) *sin|-------------------------------------|| \ \ 2 / \ 2 // \ \ 2 / \ 2 //
$$\left(- i \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}\right)$$
=
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/ 2 / 2 2 \
/ / 2 2 \ 2 2 I*atan2\2*im(a)*re(a), re (a) - im (a)/
-\/ \re (a) - im (a)/ + 4*im (a)*re (a) *e
$$- \sqrt{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}$$
-sqrt((re(a)^2 - im(a)^2)^2 + 4*im(a)^2*re(a)^2)*exp(i*atan2(2*im(a)*re(a), re(a)^2 - im(a)^2))