lect116_27rev_f11

lect116_27rev_f11 - Tuesday, November 15 Lecture 27 :...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Tuesday, November 15 Lecture 27 : Integration by substitution (Refers to Section 6.1 your text) Students who have mastered the content of this lecture know : About differentials, integration by change of variable (equivalently, by substitution). Students who have practiced the techniques presented in this lecture will be able to : Compute integrals by substitution correctly. Summary of what have learned about the notion of integration . - Our study of integration began with attempts at finding the area of the region bounded by the curve of f ( x ) and the x -axis over an interval [ a , b ]. To do this we introduced the notion of a Riemann sum. But computing areas in this way is inefficient. - The Fundamental theorem of calculus presented an alternate way to compute such numbers. This important theorem is presented into two parts. - The second part of the Fundamental theorem of calculus says that to find the area of the region bounded by the curve of f ( x ) and the x -axis over an interval [ a , b ] it suffices to find an anti-derivative of the function f ( x ), evaluating it at the limits of integration and subtracting the results. That is, if f ( x ) is continuous on [ a , b ] and F ( x ) is an anti- derivative of f ( x ) then - The first part of the Fundamental theorem of calculus says that, if f ( x ) is continuous on [ a , b ] and as x ranges over [ a , b ], then This can also be expressed by
Background image of page 1

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

View Full DocumentRight Arrow Icon
- The first part of the FTC appears to be unrelated to our initial inquiry. In these notes
Background image of page 2
Image of page 3
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 / 10

lect116_27rev_f11 - Tuesday, November 15 Lecture 27 :...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online