[SOLVED] Mathematical Expectation (Continuous Prob Dist.)

4.56 walpole

The total time, measure in units of 100 hours, that a teenager runs her stero set over a period of one year is a continuous random variable X that has the density function:

f(x) = x, 0<x<1

2-x, 1<=x<2

0, elsewhere

Evalue the mean of the random variable Y=60X^2 + 39X , where Y is equal to the number of kilowatt hours expended annually.

what i did was :

E(X) = int 0-1 x dx + int 1-2 (2-x) dx

E(X^2) = int 0-1 X^2 dx + int 1-2 x(2-x) dx

and then E(Y) = 60((EX^2)) + 39 (E(X))

but it doesn't add up to 109 (answer)

what did i do wrongly ?