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sqrt(1-(x+1)^2)
Solving integrals/ sqrt(1-(x+1)^2)

Integral of sqrt(1-(x+1)^2) dx

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You have entered [src] 
 -1/2                    
   /                     
  |                      
  |     ______________   
  |    /            2    
  |  \/  1 - (x + 1)   dx
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 /                       
 -1
∫−1−121−(x+1)2 dx\int\limits_{-1}^{- \frac{1}{2}} \sqrt{1 - \left(x + 1\right)^{2}}\, dx 
Integral(sqrt(1 - (x + 1)^2), (x, -1, -1/2))
The answer (Indefinite) [src] 
                              //                                 3                                                \
                              ||  I*acosh(1 + x)        I*(1 + x)              I*(1 + x)            |       2|    |
  /                           ||- -------------- + -------------------- - --------------------  for |(1 + x) | > 1|
 |                            ||        2               _______________        _______________                    |
 |    ______________          ||                       /             2        /             2                     |
 |   /            2           ||                   2*\/  -1 + (1 + x)     2*\/  -1 + (1 + x)                      |
 | \/  1 - (x + 1)   dx = C + |<                                                                                  |
 |                            ||                            ______________                                        |
/                             ||                           /            2                                         |
                              ||           asin(1 + x)   \/  1 - (1 + x)  *(1 + x)                                |
                              ||           ----------- + -------------------------                  otherwise     |
                              ||                2                    2                                            |
                              \\                                                                                  /
∫1−(x+1)2 dx=C+{i(x+1)32(x+1)2−1−i(x+1)2(x+1)2−1−iacosh⁡(x+1)2for ∣(x+1)2∣>11−(x+1)2(x+1)2+asin⁡(x+1)2otherwise\int \sqrt{1 - \left(x + 1\right)^{2}}\, dx = C + \begin{cases} \frac{i \left(x + 1\right)^{3}}{2 \sqrt{\left(x + 1\right)^{2} - 1}} - \frac{i \left(x + 1\right)}{2 \sqrt{\left(x + 1\right)^{2} - 1}} - \frac{i \operatorname{acosh}{\left(x + 1 \right)}}{2} & \text{for}\: \left|{\left(x + 1\right)^{2}}\right| > 1 \\\frac{\sqrt{1 - \left(x + 1\right)^{2}} \left(x + 1\right)}{2} + \frac{\operatorname{asin}{\left(x + 1 \right)}}{2} & \text{otherwise} \end{cases}
Simplify
The graph
-1.00-0.50-0.95-0.90-0.85-0.80-0.75-0.70-0.65-0.60-0.5502
Plot the graph f(x)
The answer [src] 
    ___     
  \/ 3    pi
- ----- - --
    8     12
−π12−38- \frac{\pi}{12} - \frac{\sqrt{3}}{8} 
=
= 
    ___     
  \/ 3    pi
- ----- - --
    8     12
−π12−38- \frac{\pi}{12} - \frac{\sqrt{3}}{8} 
-sqrt(3)/8 - pi/12
Numerical answer [src] 
0.478305738745259
0.478305738745259
The graph
Integral of sqrt(1-(x+1)^2) dx

    Use the examples entering the upper and lower limits of integration.

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