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# integrate sin -1[(x/a+x)1/2]

290 Points
10 years ago

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,

15 Points
3 years ago
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Yash Chourasiya
one year ago
Dear Student

Please see the solution in the attachment