Hey, everyone!

I have a test coming up next week and I'm practicing for it (so, the questions within are exclusively for my gain, not a grade) and there's a few problems on the book that I can't seem to get.

Question #1: Sketch the region enclosed by $\displaystyle \text{y}=8x+2$ and $\displaystyle \text{y}=5x^2$. Decide whether to integrate with respect to $\displaystyle \text{x}$ or $\displaystyle \text{y}$. Draw a typical approximating rectangle and label it's hight and width, then find the area of the region.

What I have done: Okay, I drew the graph and I get (by equaling both functions) that the two functions intersect at $\displaystyle (\frac{-11}{50} , \frac{6}{25})$ and at $\displaystyle (\frac{91}{50} , \frac{83}{5})$

Now, should I integrate from -11/50 to 0 and then from 0 to 91/50?

Question #2: Use Calculus to find the area of the triangle with the given vertices: $\displaystyle (0,0) , (4,1) , (-1,11)$

Here, I have no clue. I thought I could just find the midpoint between one of the segments and then the distance to the opposite vertex in order to get my height...?

There was something about this type of exercise in the "Introductory Tutorial to Multiple Integration" thread, but since we haven't done that in class, I'm not sure I can do in the test.

Sorry for the long read! I just need someone to point me in the right direction!