# Calc 2 problem involving integration

by bennwalton
Tags: calculus 2, derivative, graph analysis
 Emeritus Sci Advisor HW Helper PF Gold P: 7,808 First of all, I assume you mean f(0) = 3. How did you get 9/2 when integrating f '(x) from ‒3 to 0 ?From ‒3 to ‒2, there is an area of 1/2 above the x-axis. From ‒2 to 0, there is an area of 2, which is below the x-axis. That translated to an integral of ‒2. That gives a result of ‒3/2.In general: $$\int_a^bf'(x)\,dx=f(b)-f(a)$$ That's about all you need.