Sketch the region, R, in the first quadrant bounded by
y=7x, y=4=(x/2), y=(x-2)^2
evaluate, SS_{r}(x+y)dxdy,
what is the limits, and how do i work it out, i have sketch the region already,
In this case you have to break the integral up into three integrals - depending on what is the border of the region on the left and right.
top region: x goes from $\displaystyle \frac{y}{7}$ to $\displaystyle +\sqrt{y}+2$
middle region: x goes from $\displaystyle -\sqrt{y}+2$ to $\displaystyle +\sqrt{y}+2$
bottom region: x goes from $\displaystyle -\sqrt{y}+2$ to $\displaystyle 2y$
It might be easier to integrate the other way (dydx instead of dxdy).
- Hollywood