Class Notes (835,600)
United States (324,192)
Mathematics (589)
MATH 140 (163)
all (9)
Lecture

# Notes Integrals

5 Pages
64 Views

School
Department
Mathematics
Course
MATH 140
Professor
All Professors
Semester
Fall

Description
Notes – Integrals Aleah Pisarz 10/29 – 11/7  1 Riemann Sums: Riemann Sums are used to take the area under the curve without using integrals. When  P=x ,0 ,1 ,2 ,…3 The Lower Riemann Sum can be shown by L(P,f )=f (L) x −x +f (L) x −x +…+f (L)(x −x ) ( 1 0) ( 2 1) n n−1 where  L  is the minimum of the area defined by  xn−x n−1 The Upper Riemann Sum can be shown by U (P,f )=f (U )(x1−x 0) (U ) ( 2x +…1f (U)(x −x n n−1) where ? is the maximum of the area defined by  xn−x n−1 Ex. 1+x,0≤x≤2 f x = { 5−x,2≤ x≤4 P= {0,1,3,4 } L(P,f )=¿ 2 Notes – Integrals Aleah Pisarz 10/29 – 11/7  U (P,f )=¿ Fundamental Theorem of Calculus: If  f (x)  is continuous on  [a,b] , differentiable (a,b) ,  and f x −g(x) , then b ∫ g(x)dx=f (b)−f (a) a U­substitution: 1. Let  u  = what’s in parenthesis or under root symbols 2. Take deriv
More Less

Related notes for MATH 140
Me

OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Just a few more details

So we can recommend you notes for your school.