13112an4.11-13

# 13112an4.11-13 - c Kendra Kilmer Section 4.8...

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

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

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

Unformatted text preview: c Kendra Kilmer February 28, 2012 Section 4.8 - Antiderivatives Example 1: What are the possible functions whose derivative is x? Deﬁnition: A function F is called an antiderivative of f on an interval I if F ′ (x) = f (x) for all x in I . Theorem If F is an antiderivative of f on an interval I , then the most general antiderivative of f on I is where C is an arbitrary constant. Table of Antidifferentiation Formulas Function General Antiderivative k xn (n = −1) 1 x ex ax cos x sin x sec2 x sec x tan x csc2 x csc x cot x k f (x) f (x) ± g(x) 11 c Kendra Kilmer February 28, 2012 Example 2: Find the most general antiderivative of each function. a) f (x) = 8 b) f (x) = x5 1 c) f (x) = x4 3 d) f (t ) = 2 t9 e) f (x) = (5x4 + x3 − 2) f) f (x) = 3 + sec2 x x g) f (x) = ex + x3 3 √ 1 h) f (x) = 3 x − 2 − x 2 x i) f (x) = 4x2 + x3 8x j) f (x) = (x − 2)(x + 3) + cos x 12 c Kendra Kilmer February 28, 2012 Example 3: Find y if y(1) = 1 and dy 3 1 =+ dx x x2 Example 4: Find f (x) if f ′′ (x) = 5 − 9x, f (0) = 3, and f (1) = 10. Example 5: A car is traveling at 70 miles per hour when the brakes are fully applied, producing a constant deceleration of 40 ft/s2 . What is the distance covered before the car comes to a stop? Section 4.8 Highly Suggested Homework Problems: 1, 5, 9, 11, 13, 19, 23, 25, 27, 29, 31, 35, 37, 39, 41, 53 13 ...
View Full Document

## This note was uploaded on 04/01/2012 for the course MATH 131 taught by Professor Allen during the Fall '08 term at Texas A&M.

### Page1 / 3

13112an4.11-13 - c Kendra Kilmer Section 4.8...

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

View Full Document
Ask a homework question - tutors are online