Question

Determine value of c for which, the function is a joint pdf of 2 continuous random variables X and Y
f(x,y) = cxy \(0\leq x\leq 1\) \(x^2\leq y\leq x\)
Please, help

Answer 1

To find c, I need
\[\int_{0}^{1}\int_{x^2}^{x}cxy dydx\\
c\int_{0}^{1}\dfrac{xy^2}{2}dx |_{x^2}^{x} = \dfrac{c}{2}\int_{0}^{1}0dx\]
Which is wrong. But I don't know why. The answer from the book is c = 24