Question
xy(x^2+y^2+25)^1.5 integration limit 0<x<1 0<y<1
Answers
oobleck
∫[0,1] ∫[0,1] xy(x^2+y^2+25)^(3/2) dy dx
= ∫[0,1] 1/2 x * 2/5 (x^2+y^2+25)^(5/2) [0,1] dx
= 1/5 ∫[0,1] x ((x^2+26)^(5/2) - (x^2+25)^(5/2)) dx
now you do the 2nd integral
Note that in the first step, if u = x^2+y^2+25, ∂u/∂y = 2y(x^2+y^2+25)
= ∫[0,1] 1/2 x * 2/5 (x^2+y^2+25)^(5/2) [0,1] dx
= 1/5 ∫[0,1] x ((x^2+26)^(5/2) - (x^2+25)^(5/2)) dx
now you do the 2nd integral
Note that in the first step, if u = x^2+y^2+25, ∂u/∂y = 2y(x^2+y^2+25)