Some Integral Questions

Plato

MHF Helper
Aug 2006
22,490
8,653
Workset is due tomorrow so I gotta finish this up.

1:

I know the answer is -76/3, but I have no idea how. I tried this question 3 times and could only get close.
Attempt 1, Attempt 2, and Attempt 3.
I don't remember which was closest... I think it was two? Sorry if my work is hard to follow.

2:

View attachment 39638

I have no idea what to do with this aside from the intervals of decrease and increase, obv. I found A(0) and A(1) by essentially guessing, but I'm guessing it's the height of the rectangle used for the estimate under the given point? Cumulative area? No clue how I'd actually find these.

3:

I can't remember how to solve these and my notes are failing me,

4:

I know the first one is -5, but how do I solve the second one?
 

Plato

MHF Helper
Aug 2006
22,490
8,653
#4
\(\displaystyle \int_4^7 {f\;dx} + \boxed{\int_7^{10} {f\;dx} } + \int_{10}^{13} {f\;dx} = \int_4^{13} {f\;dx} \)
Can you fill in details?