Integral of √(a^2-x^2) dx
The solution
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−x2dx=C+⎩⎨⎧−2ia2acosh(ax)−2−1+a2x2iax+2a−1+a2x2ix32a2asin(ax)+2ax1−a2x2fora2x2>1otherwise
Use the examples entering the upper and lower limits of integration.