lect116_25rev_f11

# lect116_25rev_f11 - Thursday November 10 Lecture 25...

This preview shows pages 1–2. Sign up to view the full content.

Thursday, November 10 Lecture 25 : Fundamental theorem of calculus. (Refers to Section 5.4, 5.5 in your text) Students who have mastered the content of this lecture know : The Fundamental theorem of calculus, the definition of “antiderivative” and the general antiderivative of a function f(x), the net change of a function over an interval [a, b]. Students who have practiced the techniques presented in this lecture will be able to : State both parts of the FTC and apply the FTC directly to integrals, compute the definite of integral of a simple function by first finding an antiderivative of the function, compute the net change of a function over an interval. The Fundamental theorem of calculus is a theorem which links “differential” calculus to “integral” calculus. It shows that differentiation (finding slopes of tangent lines to a curve) and integration (computing areas of regions), two apparently unrelated processes are actually inverses of each other. Note: It is important to note that the FTC is actually two statements. We often refer to them as “Part I and Part II of the FTC”. But different authors may choose to order them differently. So in a different text look carefully to determine how the author prefers to order them. 25.1 The Fundamental theorem of calculus (FTC) – Let f be continuous on the interval [ a , b ] and g ( x ) be the function defined as Then: 1) The function g ( x ) is continuous on [ a , b ] and differentiable on ( a , b ) and for any x strictly between a and b , g ( x ) = f ( x ).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 12/28/2011 for the course MATH 116 taught by Professor Robertandre during the Spring '11 term at Waterloo.

### Page1 / 6

lect116_25rev_f11 - Thursday November 10 Lecture 25...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online