Question

Using FTC(fundamental theory of calculus) evaluate the derivative of:

(definte integral- lower bound 0 and upper 2) ∫|2x-1|dx

I have no idea how to do this, especially because the dx is on the same side of the equation. It is usually d/dx, but this is also on the other side. I also graphed the absolute value function and the area under the interval [0,2] is kind of in two different separate regions.
Please provide steps with the thought process. Thank you so much!

Answer 1

"I also graphed the absolute value function and the area under the interval [0,2] is kind of in two different separate regions."

Good. You have to separate it into two integrals for each region. For x < 0.5, |2x-1| = 1-2x. For x >= 0.5, |2x-1| = 2x-1.

Integrate 1-2x from 0 to 0.5, and integrate 2x-1 from 0.5 to 2.