Density function for continuous random variables

[cue928]

For the density function for random variable Y:
f(y) = cy^2 for 0<= y <= 2; 0 elsewhere
We are asked to find the value of c. I did a definite integral from 0 to 2 of cy^2. I get c = 3/8. Why would the book show an answer of c = 1/8? Is this an error on their part or am I missing something stupid?

 

[nonequilibrium]

Indeed, I also think it's an error in the book.