Question

@perl

Answer 1

draw the function on a graph and then find the area under the curve using geometry

Answer 2

did you get 13.5? @perl

Answer 3

@ybarrap can you pleaseee check my answer??

Answer 4

So what does f(x) look like?

We know for \(x\le3\) that \(f(x)\) is equal to 3. But where does it start? Look at the lower limit of your integral. Where does it start? It starts at 0. f(x) is equal to 3 between 0 and 3. Hey, that's just a square! You know the area of a 3x3 square?

Next you are given for \(x>3\) that \(f(x)=6-x\).

What does this mean?

Well, we start at \(about\) 3, that means f(3)=3 and then \(x\) starts to get larger. If this happens, f(x) starts to get smaller because 6-x gets smaller. Kool, so does this go on forever? I mean, does x go on and on?

No. Look at the limit of your integral. What is the upper limit? It's 6. So we stop at 6.

So the 1st part of your integral is the area of a 3x3 square. You add to this thing that starts at 3 and goes all the way down to 6-6 (because, 6 is the upper limit of the integral), that's 0 (of course). What is that shape?



Hey! That's just a triangle with a base of 3 and a height of 3!

Easy, right?!