Given....sqrt(4y^2+5)*y dy
let.........4y^2+5=u
du/dy=8y
dy=du/8y
int u*ydy=int u^1/2*y*du/8y
=int u^1/2 du/8
=1/8intu^1/2 du
=1/8[u^(3/2)/(3/2)]
considering the boundaries (1,0)
=1/8[2/3]
=1/12
there fore the intergral of sqrt(4y^2+5)*y dy with boundaries at 1 and 0=1/12