I = int sqrt(4y^2 + 5) dx dy, bounded on [0 .. y] and [0 .. 1]
Rewrite this as
I1 = int[0 .. y] sqrt(4y^2 + 5) dx
and I2 = int[0 .. 1] I1 dy
with I = I2.
I1 = int[0 .. y] sqrt(4y^2 + 5) dx = {sqrt(4y^2+ 5)*x}[0 .. y] = {sqrt(4y^2 + 5)*y - {0)}
I1 = sqrt(4y^2 + 5)*y
I2 = int[0 .. 1] I1 dy = int [0 .. 1] sqrt(4y^2 + 5)*y dy = {(1/12)(4y^2 + 5)^(3/2)}[0 .. 1]
I2 = {(1/12)(4 + 5)^(3/2)) - (1/12)(5^(3/2))} = (1/12){9^(3/2) - 5*5^(1/2)}
I2 = (1/12){27 - 5*sqrt(5)}
I2 = 9/4 - (5/12)*sqrt(5)
I = 9/5 - (5/12)*sqrt(5)