Determining the joint density function -- what's wrong with my solution? Let $T_1$ be the time between a car accident and the claim reported to the insurance company. Let $T_2$ be the time between the report of the claim and payment of the claim. The joint density function of $T_1$ and $T_2$, $f(t_1, t_2)$,  is constant over the region $0<t_1, t_2<6, t_1+t_2<10$ and zero otherwise. Determine $f(t_1, t_2)$.
My attempt: Let $f(t_1, t_2) = k$. Then,
$$\int_0^6 \int_0^{10-y} k \; dx\; dy = \int_0^6 k(10-y) \; dy = 1 \implies k\left[60-\frac{35}{2}\right] = 1$$
which ultimately gives $k = \frac{1}{42}$, however, the correct answer is $k = \frac{1}{34}$. Where have I gone wrong?

Blue line: the area on which you should have integrated.
Orange line: the area on which you actually integrated.

