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integrate sin -1[(x/a+x)1/2]
Hi Suchita,
Make the substitution, x = a*tan2θ
So dx = 2a*tanθ*sec2θ dθ
and x/(a+x) = sin2θ
∫θ*2a*tanθ*sec2θ dθ = 2a∫θ secθ*(secθtanθ) dθ.
Integrate this by parts
= a*[θsec2θ - ∫sec2θdθ] = a[θsec2θ - tanθ] + constant.
where sec2θ = 1 + (x/a), and tanθ = √(x/a), θ = tan-1√(x/a)
Hope that helps.
All the best,
Regards,
Ashwin (IIT Madras).
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