Science:Math Exam Resources/Courses/MATH200/December 2011/Question 06/Hint 2

To find the integration boundaries of the variables $\displaystyle x,\ y$ for the region $\displaystyle R$ a sketch is very helpful

On the sketch we see that the region $\displaystyle R$ is bounded by the functions $\displaystyle y=2-x$ and $\displaystyle y=2-2x$

If we do not want to split the region into two integrals, we must integrate with respect to $\displaystyle x$ first. Find the $\displaystyle y$-depending boundaries for $\displaystyle x$, such that

$\displaystyle {\begin{aligned}{\underline {\ \ \ \ \ \ \ }}&\leq x\leq {\underline {\ \ \ \ \ \ \ \ }}\\0&\leq y\leq 2\end{aligned}}$