Question

Here comes the question again

Answer 1

\[\int \sqrt{(a-x)(x-b)}dx\]Let y=x-b
dy = dx
a-x =a - (y+b) = a-b-y
So,
\[\int \sqrt{(a-x)(x-b)}dx\]\[=\int \sqrt{(a-b-y)(y)}dy\]\[=\int \sqrt{-y^2 +(a-b)y}dy\]\[=\int \sqrt{y}\sqrt{-y +(a-b)}dy\]\[=\int \sqrt{y}\sqrt{-y}\sqrt{\frac{-y +(a-b)}{-y}}dy\]
See?! Something's wrong here!

Answer 2

@experimentX

Answer 3

\[ =\int \sqrt{y}\sqrt{-y +(a-b)}dy \\
=\int \sqrt{y^2}\sqrt{-1 +{(a-b)\over y}}dy\]

Answer 4

i was wondering if ... i could get rid of y^2

Answer 5

Phew.. my bad. Sorry. Go and do your work now :S