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!
"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.