This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: F(b) plug in x=b to F(x) (notice this is anti-derivative) F(a) plug in x=a to F(x) NOTE: There is no +C involved for definite integrals; in particular when using FTC. This is because definite integral answers are not equations. 3. Ex(FTC)-- Evaluate each integral. (a) dx (b) dx (c) dx (d) dx (e) dx (f) dx <Answers> (a) = (b) D.I. not possible because f(x) is not continuous at x=0, have a bad interval (c) = 3 ln2 = ln8 (d) = = (e) = 4 (f) = 2e 3 + 1 4. Ex(FTC and integral properties) Find the area of the shaded region made by the equations y1 and y2 for their respective intervals. Given: y1 = and y2 = x 2 <Answer> Set up the integrals (notice the proper form of the notation): Evaluate the integrals: = and = Sum of the two D.I.'s: 2/3 + 7/3 = 3 The area of the shaded region. 1 1 2 4 x y2 y1...
View Full Document
This note was uploaded on 02/21/2011 for the course MATH 408C taught by Professor Knopf during the Spring '10 term at University of Texas at Austin.
- Spring '10
- Fundamental Theorem Of Calculus