Answer
$\dfrac{21}{2}$
Work Step by Step
Since, $dS=\sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dt})^2} dt$
Here, $\dfrac{dx}{dt}=(2t+3)^{1/2}$
and $\dfrac{dy}{dt}=1+t$
Thus,
$S=\int_{0}^{3} \sqrt{((2t+3)^{1/2})^2+(1+t)^2} dt=\int_{0}^{3} (t+2) dt$
Thus,
$S=[\dfrac{t^{2}}{2}+2t]_{0}^{3} =\dfrac{9}{2}+(2)(3)=\dfrac{21}{2}$
