Sr Examen

Otras calculadoras

Resolución de integrales/ a-x^2/ 1/sqrt/ 1/sqrt((a-x^2))

Integral de 1/sqrt((a-x^2)) dy

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1               
  /               
 |                
 |       1        
 |  ----------- dx
 |     ________   
 |    /      2    
 |  \/  a - x     
 |                
/                 
0
∫011a−x2 dx\int\limits_{0}^{1} \frac{1}{\sqrt{a - x^{2}}}\, dx 
Integral(1/(sqrt(a - x^2)), (x, 0, 1))
Respuesta (Indefinida) [src] 
                        //                     | 2|    \
                        ||        /  x  \      |x |    |
  /                     ||-I*acosh|-----|  for |--| > 1|
 |                      ||        |  ___|      |a |    |
 |      1               ||        \\/ a /              |
 | ----------- dx = C + |<                             |
 |    ________          ||      /  x  \                |
 |   /      2           ||  asin|-----|     otherwise  |
 | \/  a - x            ||      |  ___|                |
 |                      ||      \\/ a /                |
/                       \\                             /
∫1a−x2 dx=C+{−iacosh⁡(xa)for ∣x2a∣>1asin⁡(xa)otherwise\int \frac{1}{\sqrt{a - x^{2}}}\, dx = C + \begin{cases} - i \operatorname{acosh}{\left(\frac{x}{\sqrt{a}} \right)} & \text{for}\: \left|{\frac{x^{2}}{a}}\right| > 1 \\\operatorname{asin}{\left(\frac{x}{\sqrt{a}} \right)} & \text{otherwise} \end{cases}
Simplificar
Respuesta [src] 
  1                                      
  /                                      
 |                                       
 |  /                            2       
 |  |        -I                 x        
 |  |--------------------  for --- > 1   
 |  |           _________      |a|       
 |  |          /       2                 
 |  |  ___    /       x                  
 |  |\/ a *  /   -1 + --                 
 |  |      \/         a                  
 |  <                                  dx
 |  |         1                          
 |  |-------------------    otherwise    
 |  |           ________                 
 |  |          /      2                  
 |  |  ___    /      x                   
 |  |\/ a *  /   1 - --                  
 |  |      \/        a                   
 |  \                                    
 |                                       
/                                        
0
∫01{−ia−1+x2afor x2∣a∣>11a1−x2aotherwise dx\int\limits_{0}^{1} \begin{cases} - \frac{i}{\sqrt{a} \sqrt{-1 + \frac{x^{2}}{a}}} & \text{for}\: \frac{x^{2}}{\left|{a}\right|} > 1 \\\frac{1}{\sqrt{a} \sqrt{1 - \frac{x^{2}}{a}}} & \text{otherwise} \end{cases}\, dx 
=
= 
  1                                      
  /                                      
 |                                       
 |  /                            2       
 |  |        -I                 x        
 |  |--------------------  for --- > 1   
 |  |           _________      |a|       
 |  |          /       2                 
 |  |  ___    /       x                  
 |  |\/ a *  /   -1 + --                 
 |  |      \/         a                  
 |  <                                  dx
 |  |         1                          
 |  |-------------------    otherwise    
 |  |           ________                 
 |  |          /      2                  
 |  |  ___    /      x                   
 |  |\/ a *  /   1 - --                  
 |  |      \/        a                   
 |  \                                    
 |                                       
/                                        
0
∫01{−ia−1+x2afor x2∣a∣>11a1−x2aotherwise dx\int\limits_{0}^{1} \begin{cases} - \frac{i}{\sqrt{a} \sqrt{-1 + \frac{x^{2}}{a}}} & \text{for}\: \frac{x^{2}}{\left|{a}\right|} > 1 \\\frac{1}{\sqrt{a} \sqrt{1 - \frac{x^{2}}{a}}} & \text{otherwise} \end{cases}\, dx 
Integral(Piecewise((-i/(sqrt(a)*sqrt(-1 + x^2/a)), x^2/|a| > 1), (1/(sqrt(a)*sqrt(1 - x^2/a)), True)), (x, 0, 1))

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

    © Sr Examen – Калькулятор