Question Number 101531 by mhmd last updated on 03/Jul/20

find ∫(√(ax−x^2 ))dx

Answered by Mr.D.N. last updated on 03/Jul/20

I = ∫(√(ax−x^2 ))dx = ∫(√(−(x^2 −ax))) dx = ∫ (√(((a/2))^2 −(x−(a/2))^2 )) dx = (((x−(a/2))(√(((a/2))^2 −(x−(a/2))^2 )))/2) + ((((a/2))^2 )/2)sin^(−1) (((x−(a/2)))/(a/2))+C = ((((2x−a)/2)(√(ax−x^2 )))/2) + (a^2 /8) sin^(−1) ((2x−a)/a)+C = (((2x−a)(√(ax−x^2 )))/4) + (a^2 /8) sin^(−1) (((2x−a))/a) +C//.

Commented bymhmd last updated on 03/Jul/20

thank you sir