Hello, I have a question about conditional distributions in the continuous case.

We are given that the joint distribution function of two continuous random variables X and Y is

$\displaystyle f(x,y) = \frac{3}{2}(x^2+y^2) $ for $\displaystyle \;\;0 \leq x \leq 1 , 0 \leq y \leq 1$

The marginal distribution of Y can be found by integrating with respect to x, the marginal distribution of Y is

$\displaystyle f_Y(y) = \frac{3}{2}y^2+\frac{1}{2}$ for $\displaystyle 0 \leq y \leq 1$

The book asks to find the conditional density of X given that Y =.3

This is the answer that is listed in the book

$\displaystyle f_{X|Y}(x|Y =.3) = \frac{f(x,.3)}{f_Y(.3)} = \frac{\frac{3}{2}(x^2+.3^2)}{\frac{3}{2}*.3^2+.5}= \frac{\frac{3}{2}(x^2+.09)}{.635}$

Why is the book just plugging in the value .3 for y? Shouldn't we be integrating since this is continous?