1.

int_0^1(x^5(4-x^2))/sqrt(1-x^2)dx

Answer»

Solution :`int_0^1(x^5(4-x^2))/SQRT(1-x^2)DX`
=`int_0^(pi/2)(sin^5theta(4-sin^2theta))/costheta.costhetad THETA` (where `x=sintheta`
`rArr dx=costhetad theta`)
=`4int_0^(pi/2)sin^5thetad theta-int_0^(pi/2)sin^7thetad theta`
=`4 CDOT 4/5 cdot 2/3 - 6/7 cdot 4/5 cdot 2/3`
=`8/15(4-6/7)=8/15cdot22/7=(176)/105`


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