1.

Integrate the following functions sqrt(1-4x-x^2)

Answer»

Solution :`int SQRT(1-4x-x^2) dx`
=`int sqrt(1-(x^2+4x))dx`
=`int sqrt(1-(x^2+4x+4-4) dx`
=`int sqrt(1-(x+2)^2+4) DX`
=`int sqrt((sqrt5)^2-(x+2)^2) dx`
`(x+2)/2 sqrt((sqrt)^2-(x+2)^2) + (sqrt5)^2/2 sin^-1((x+2)/sqrt5) +C`
`(x+2)/2 sqrt(1-4x-x^2)+ 5/2 sin^-1((x+2)/sqrt5)+c`


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