5.3 - Fundamental Theorem of Calculus

Question 1

What is the first part of the FTC?

Answer 1

The first part of FTC deals with functions defined by an equation of the form
g(x) = ∫(x-a) f(t)dt
where f is continuous on [a,b] & x varies between a&b. Observe that g depends only on x which appears as the variable upper limit in the integral

Question 2

What is the first part of the Definition of FTC?

Answer 2

f is continuous on [a,b], then the function g defined by

g(x) = ∫(x-a) f(t)dt a0) g(x+h) - g(x)/h = f(x)

Question 3

What is the second part of the Definition of FTC?

Answer 3

if f is continuous on [a,b], then
∫(b-a) f(x) = F(b) = F(a)
where F is any antiderivative of f, that is a function such that F’ = f