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(%i1)
f
:
sqrt
((
x
-
a
)
*
(
b
-
x
))
/
x
;
\[\tag{$f$}\label{f}\frac{\sqrt{\left( b-x\right) \,\left( x-a\right) }}{x}\]
(%i2)
assume
(
a
<
b
)
;
\[\tag{$\%{}o2$}\label{o2} [b < a]\]
(%i3)
assume
(
a
>
0
)
;
\[\tag{$\%{}o3$}\label{o3} [a > 0]\]
(%i4)
integrate
(
f
,
x
,
a
,
b
)
;
\[\tag{$\%{}o4$}\label{o4} -\left( -b-a\right) \,\operatorname{asin}\left( \frac{\sqrt{{{b}^{2}}-2ab+{{a}^{2}}}}{b-a}\right) -2\sqrt{a}\,\sqrt{b}\,\operatorname{asin}\left( \frac{\sqrt{{{b}^{2}}-2ab+{{a}^{2}}}}{b-a}\right) \]
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