0223 - Math 31A 2010.02.23 MATH 31A DISCUSSION JED YANG 1....

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 31A 2010.02.23 MATH 31A DISCUSSION JED YANG 1. Basic Integration 1.1. Exercise 5.1.71. Describe the area represented by the limit lim N →∞ 3 N N summationdisplay j =1 parenleftbigg 2 + 3 j N parenrightbigg 4 . Solution. Consider the area under the curve f ( x ) from x = a to x = b . We divide the interval b − a into N equal slots, so each slot has width Δ x = b- a N . The right end points of the j th rectangle is a + j Δ x . The value of the function at the right end point of the j th rectangle is therefore f ( a + j Δ x ). If we use these as the height of the rectangles, then the area of the j th rectangle is Δ x · f ( a + j Δ x ). We sum this up to get ∑ N j =1 Δ x · f ( a + j Δ x ). We can factor out the width of the rectangles as they are all the same. Thus we get Δ x ∑ N j =1 f ( a + j Δ x ). If we let N goes to infinity, the approximation becomes finer and finer, and approaches the area under the curve....
View Full Document

This note was uploaded on 09/19/2011 for the course MATH 31A taught by Professor Jonathanrogawski during the Winter '07 term at UCLA.

Page1 / 2

0223 - Math 31A 2010.02.23 MATH 31A DISCUSSION JED YANG 1....

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

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