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Solving integrals/ sqrt(r^2-x^2)

Integral of sqrt(r^2-x^2) dx

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  1                
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∫01r2−x2 dx\int\limits_{0}^{1} \sqrt{r^{2} - x^{2}}\, dx 
Integral(sqrt(r^2 - x^2), (x, 0, 1))
The answer (Indefinite) [src] 
                         //     2      /x\                                                        \
                         ||  I*r *acosh|-|              3                                 | 2|    |
                         ||            \r/           I*x                 I*r*x            |x |    |
                         ||- ------------- + ------------------- - -----------------  for |--| > 1|
                         ||        2                   _________           _________      | 2|    |
  /                      ||                           /       2           /       2       |r |    |
 |                       ||                          /       x           /       x                |
 |    _________          ||                  2*r*   /   -1 + --    2*   /   -1 + --               |
 |   /  2    2           ||                        /          2        /          2               |
 | \/  r  - x   dx = C + |<                      \/          r       \/          r                |
 |                       ||                                                                       |
/                        ||                                    ________                           |
                         ||                                   /      2                            |
                         ||                                  /      x                             |
                         ||              2     /x\   r*x*   /   1 - --                            |
                         ||             r *asin|-|         /         2                            |
                         ||                    \r/       \/         r                             |
                         ||             ---------- + ------------------                otherwise  |
                         \\                 2                2                                    /
∫r2−x2 dx=C+{−ir2acosh⁡(xr)2−irx2−1+x2r2+ix32r−1+x2r2for ∣x2r2∣>1r2asin⁡(xr)2+rx1−x2r22otherwise\int \sqrt{r^{2} - x^{2}}\, dx = C + \begin{cases} - \frac{i r^{2} \operatorname{acosh}{\left(\frac{x}{r} \right)}}{2} - \frac{i r x}{2 \sqrt{-1 + \frac{x^{2}}{r^{2}}}} + \frac{i x^{3}}{2 r \sqrt{-1 + \frac{x^{2}}{r^{2}}}} & \text{for}\: \left|{\frac{x^{2}}{r^{2}}}\right| > 1 \\\frac{r^{2} \operatorname{asin}{\left(\frac{x}{r} \right)}}{2} + \frac{r x \sqrt{1 - \frac{x^{2}}{r^{2}}}}{2} & \text{otherwise} \end{cases}
Simplify

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

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