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Solving integrals/ √(a^2-x^2)

Integral of √(a^2-x^2) dx

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∫01a2−x2 dx\int\limits_{0}^{1} \sqrt{a^{2} - x^{2}}\, dx 
Integral(sqrt(a^2 - x^2), (x, 0, 1))
The answer (Indefinite) [src] 
                         //     2      /x\                                                        \
                         ||  I*a *acosh|-|              3                                 | 2|    |
                         ||            \a/           I*x                 I*a*x            |x |    |
                         ||- ------------- + ------------------- - -----------------  for |--| > 1|
                         ||        2                   _________           _________      | 2|    |
  /                      ||                           /       2           /       2       |a |    |
 |                       ||                          /       x           /       x                |
 |    _________          ||                  2*a*   /   -1 + --    2*   /   -1 + --               |
 |   /  2    2           ||                        /          2        /          2               |
 | \/  a  - x   dx = C + |<                      \/          a       \/          a                |
 |                       ||                                                                       |
/                        ||                                    ________                           |
                         ||                                   /      2                            |
                         ||                                  /      x                             |
                         ||              2     /x\   a*x*   /   1 - --                            |
                         ||             a *asin|-|         /         2                            |
                         ||                    \a/       \/         a                             |
                         ||             ---------- + ------------------                otherwise  |
                         \\                 2                2                                    /
∫a2−x2 dx=C+{−ia2acosh⁡(xa)2−iax2−1+x2a2+ix32a−1+x2a2for ∣x2a2∣>1a2asin⁡(xa)2+ax1−x2a22otherwise\int \sqrt{a^{2} - x^{2}}\, dx = C + \begin{cases} - \frac{i a^{2} \operatorname{acosh}{\left(\frac{x}{a} \right)}}{2} - \frac{i a x}{2 \sqrt{-1 + \frac{x^{2}}{a^{2}}}} + \frac{i x^{3}}{2 a \sqrt{-1 + \frac{x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{x^{2}}{a^{2}}}\right| > 1 \\\frac{a^{2} \operatorname{asin}{\left(\frac{x}{a} \right)}}{2} + \frac{a x \sqrt{1 - \frac{x^{2}}{a^{2}}}}{2} & \text{otherwise} \end{cases}
Simplify

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

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