What is a strategy to evaluate INT(sqrt(a-x^2)dx) ?

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What is a strategy to evaluate INT(sqrt(a-x^2)dx) ?

Mathematics
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put x= a sin(t)
i'm the least experienced with trig substitution, can you show me the next step? my problem is that i keep ending up with two terms under the sqrt and they don't make another trig identity.
x= a sin(t) dx/dt= a cost

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dx= a cost dt
i imagine what i'm trying to get is a trig function squared under the square root so that they cancel, is there another way that would get rid of that square root?
here is what u get
hey in ur question is it a or a^2?
a
ok...do integration by parts..u know how to do that.......I've done it on paper ..it works
so x=sin (t), and int by parts as well?
no just integration by parts without any substitution
so u=a-x^2 and dv=sqrt(u)du ?
dont substitute, take the whole square root thing as first term and 1 as second term. okay?
i don't get it, it just seems to prolong the problem. i still have two terms under the sqrt.

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