MAT 1300 Lecture 13: MAT 1300 LECTURE 13 - THE FUNDAMENTAL THEOREM AND ANTIDIFFERENTIATION

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1300
• Professor: Hung-Chang Liao

Document Summary

Mat 1300 lecture 13 - the fundamental theorem and antidifferentiation. Recall that if f(x) represents the distance travelled then f"(x) represents the speed. On the other hand we"ve seen that the definite integral of f"(x) over [a,b], b a. Represents the total distance travelled between time a and time b . therefore b a. Let f be a differentiable function . then b a. This gives a powerful method to compute a definite integral b a f(x) dx. We only need to find a function f(x) such that f"(x)= f(x) then compute f(b) -f(a) Example : find a function f such that f"(x)= 2x. Notice that f(x) =x 2 + 1 also works . In fact f(x) =x 2 +c for any number c works just fine. An antiderivative of a function f(x) is any function f such that f"(x) = f(x)