00:01
So the main thought on this first problem is that if you're starting at 0 and you need 3 subintervals, you better count by 2s.
00:10
But we actually don't even need the 6 because the directions ask for the left riemann sum.
00:15
So if you plugged in 0, 3 times 0 squared is 0.
00:19
Plug in 2 for x, so 2 squared is 4 times 3 is 12.
00:23
And then 16, that's 4 squared times 3, should be 48.
00:28
Let me double check that one.
00:30
3 times 4 squared, yep, that's 48.
00:33
So now the sum of those three rectangles, each width has 2 and you multiply by the number on the left.
00:41
Plus the next width of 2 times the number on the left.
00:46
Which is why we didn't need at 6.
00:49
So really all i have to do is just worry about 24, that's 2 times 12, and then 2 times 48, i think is 96.
00:57
I ended up with an answer of 120.
00:59
So looking at the next problem, where we're doing the integral from negative 4 to 6, g of x dx.
01:12
Circles and lines.
01:14
So if you look at that circle, first of all it's below the x axis, so it's negative...