P paulinatran10 Guest Jan 19, 2009 #1 Integrate: (x^2+1)^(1/2) .... I think it involves some kind of multiplying by the conjugate or whatever, but I'm not sure where that gets me. Can someone please help?? THannkkk you!
Integrate: (x^2+1)^(1/2) .... I think it involves some kind of multiplying by the conjugate or whatever, but I'm not sure where that gets me. Can someone please help?? THannkkk you!
H H Guest Jan 19, 2009 #2 ANTI DERIVATIVE OF (x^2 + 1) ^ 1/2 a = x^2 + 1 da = 2x 1/2 antiderivative of (x^2 + 1) ^ 1/2 2x dx = 1/2 (x^2 + 1)^3/2 / (3/2) = (x^2+1)^(3/2) all over 3 is the antiderivative of that function
ANTI DERIVATIVE OF (x^2 + 1) ^ 1/2 a = x^2 + 1 da = 2x 1/2 antiderivative of (x^2 + 1) ^ 1/2 2x dx = 1/2 (x^2 + 1)^3/2 / (3/2) = (x^2+1)^(3/2) all over 3 is the antiderivative of that function
T Track P Guest Jan 19, 2009 #3 y =√ x²+1 is hyperbola. The integral will inevitably involve hyperbolic functions. Armed with this knowlege use variable sh(u) = x dx = ch(u) du y = √sh²u + 1 = √ch²u = ch(u) ∫√ x²+1 dx = ∫ ch(u) ch(u) du = ∫ 1/2 (ch(2u) - 1) du
y =√ x²+1 is hyperbola. The integral will inevitably involve hyperbolic functions. Armed with this knowlege use variable sh(u) = x dx = ch(u) du y = √sh²u + 1 = √ch²u = ch(u) ∫√ x²+1 dx = ∫ ch(u) ch(u) du = ∫ 1/2 (ch(2u) - 1) du
