# 2nd fundamental theorem of calculus

by snakehunter
Tags: calculus, fundamental, theorem
 P: 617 Do you need to understand the proofs? Or just understand the idea? FTC#2 says $\int^b_a f(x)dx = F(b) - F(a)$ where the anti-derivative of f(x) is F(x) So what you are probably using this Thrm for is evaluating definite integrals (ones with A and B stated). So what you do is find the anti-derivative of f(x) i.e. F(x), and then evaluate that anti-derivative at a and b, then take the absolute value of their difference. For example if we wanted to evaluate: $\int^5_1 3x^2dx$ we would first find the anti derivative of 3x^2. Which is x^3. Then we would evaluate x^3 at 1 and 5 which gives us, 1 and 125. We subtract 1 from 125 and get 124, hence: $\int^5_1 3x^2dx = 124$