Applications of Integration · Medium problem

$\displaystyle\int_0^2\sqrt{1+4y^2}\,dy$

$\displaystyle\int_0^{3}\sqrt{1+4y^2}\,dy$

$\displaystyle\int_0^4\sqrt{1+4y^2}\,dy$

$\displaystyle\int_0^2\sqrt{1+4y^3}\,dy$