1.

Integrate the following int_0^1x^7/sqrt(1-x^2)dx

Answer»

Solution :`int_0^1x^7/sqrt(1-x^2)DX`
=`int_0^(pi/2)(sin^7theta.costhetad theta)/costheta (where `x=sintheta`
`rArr dx=costhetad theta`)
=`int_0^(pi/2)sin^7thetad theta=6/7 . 4/5 . 2/3=(48)/105`


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