Review-Test2

Wikimediaorgwikipediacommons22a x

This preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: 1.  Approximated By Rectangles 2.  Calculated By Area of Shapes 3.  Anti-derivatives Integration Approximated by Rectangles (here 4 rectangles) http://en.wikipedia.org/wiki/Riemann_sum Left Endpoints http://en.wikipedia.org/wiki/Riemann_sum Right Endpoints Add up the area of all the rectangles lim+lim eln(= = limy y= lim+ xx = 11 e y ) lim =x!0 + x = lim x! 0 x ! 0+ + + x! 0 x!0 x!0 100100 ✓ X X✓ ◆ ◆ 11 11 b i i i i +11 + i=1 i=1 a n X n X i, i=1 n X If we use enough rectangles… n X n n i,X i2 , X i3 i2 , i=1 i3 i=1 Area of each Zb n rectangle http://upload.wikimedia.org/wikipedia/commons/2/2a/ X Riemann_sum_convergence.png f (x) dx = lim n f (xi ) x Z i=1 i=1 ba i=1 f (x) dx = lim n!1 a where X i=1 n!1 x= b a n f ( xi ) x i=1 , xi = a + i x Definition of an integral as a Reimann sum Integration using Shapes Integration Using anti-derivatives ¤༊ See table on page 398 of your textbook for the ones your should have memorized. ¤༊ Substitution i...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online