ज्ञात करें `int sqrt(4-x^2) dx`

Explanation

माना की `I=int 1sqrt(4-x^2)dx` तो `I=int 1sqrt(4-x^2)`
`=x sqrt(4-x^2) - int x ""1/2 ( 4-x^2)^("-1/2")(-2x)dx`
`=x sqrt(4-x^2) - int (-x^2)/sqrt(4-x^2) dx = x sqrt(4-x^2) -int ((4-x^2)-4)/sqrt(4-x^2)dx`
`=xsqrt(4-x^2) - int sqrt(4-x^2) dx + 4 int (dx)/sqrt(4-x^2)`
`:." "I x sqrt(4-x^2) -I +4 int (dx)/sqrt(4-x^2)`
या, `2I=xsqrt(4-x^2)+4int(dx)/sqrt(2^2-x^2)=xsqrt(4-x^2)+4 sin^(-1)(x/2)+c_1`
`:." "I=(xsqrt(4-x^2))/2+2sin^(-1)(x/2)+c` जहां `c=c_1/2`