Please Integrate the following definite integral:

      - 1 1     x 1   -   x 2 ,   sin - 1   2 x   1   -   x 2 .   d x

Dear Student,
Please find below the solution to the asked query:

I=-11x1-x2sin-12x1-x2Let x=sintas x goes from -1 to 1, hence t goes from -π2 to π2I=-π2π2 sint1-sin2tsin-12sint1-sin2t=-π2π2 sint1-sin2tsin-12sint1-sin2t=-π2π2 sintcostsin-12sintcost=-π2π2 tant sin-1sin2t=2-π2π2 t.tantThe integration of  t.tant is not possible because t.tant  is not integrablein terms of elementary function which are taught to us.

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