Answer
$\dfrac{63}{4}$
Work Step by Step
Let us consider that two continuous functions $f(x)$ and $g(x)$ with $f(x)\geq g(x)$ on the interval $[a,b]$ . The area (A) of the region bounded by the graph of $f(x)$ and $g(x)$ on the interval $[a,b]$ can be calculated as: $Area(A)=\int_a^b [f(x)-g(x)] \ dx$
Thus, the area of the region is:
$A=\int_a^b [f(x)-g(x)] \ dx\\ = \int_{0}^{3} [\dfrac{y+15}{2}-y^2] \ dy \\= [\dfrac{y^2}{4}+\dfrac{15y}{2}-\dfrac{y^3}{3}]_{0}^3 \\= \dfrac{9}{4}+\dfrac{45}{2}-9 \\=\dfrac{63}{4}$