The correct option is C 15
We have seen that if g(y)≥0 for yϵ [c, d] then the area bounded by curve x = g(y) and y-axis between abscissa y = c and y = d is ∫dcg(y)dy .
We'll use the same concept here. Here the curve given is
x=y2+2 and c = 0 &d=3.So,g(y)≥0 ∀x∈(0,3)
Let the area enclosed be A.
A=∫30(y2+2)dy.
A=(y33+2y)|30A=9+6−0A=15