How do you integrate \sqrt{1-x^2}

Ernest Ryland

Ernest Ryland

Answered question

2021-12-17

How do you integrate 1x2

Answer & Explanation

Thomas White

Thomas White

Beginner2021-12-18Added 40 answers

The answer is =12arcsinx+12x1x2+C
Explanation:
Let x=sinθ,,dx=cosθdθ
cosθ=1x2
sin2θ=2sinθcosθ=2x1x2
Therefore, the integral is
I=1x2dx=cosθcosθdθ
=cos2θdθ
cos2θ=2cos2θ1
cos2θ=1+cos2θ2
Therefore,
I=12(1+cos2θ)dθ
=12(θ+12sin2θ)
=12arcsinx+12x1x2+C
Juan Spiller

Juan Spiller

Beginner2021-12-19Added 38 answers

Ill
RizerMix

RizerMix

Expert2021-12-29Added 656 answers

I=11x2dx=dx1x2(1x2dxdx)dx
=x1x22x21x2x dx
=x1x2+1(1x2)1x2dx
=x1x2+11x2dxI
Now, 11x2dx=arcsinx+C

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