lesson 5 Integration of Exponential Function

lesson 5 Integration of Exponential Function - a ln 1 du a...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
INTEGRATION OF EXPONENTIAL FUNCTION
Background image of page 1

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

View Full DocumentRight Arrow Icon
INTEGRATION OF EXPONENTIAL FUNCTION Define exponential functions; Illustrate an exponential function; Differentiate exponential function from other transcendental function function ; provide correct solutions for problems involving exponential functions; and Apply the properties of exponential functions. OBJECTIVES:
Background image of page 2
functions l exponentia of Properties : call Re ( 29 x e . 6 x e ln 5. y ln x if y e 4. 1 e ln 3. x all for x, e ln 2. 0 x for , x e 1. x ln x x x lnx = = = = = = = ( 29 ab b a b - a b a b a b a a ln x x e e . 10 e e e . 9 e e e . 8 0 a for , e a . 7 = = = = +
Background image of page 3

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

View Full DocumentRight Arrow Icon
( 29 du e e d : call Re u u = ( 29 = u u e d du e side each of integral the Evaluate C e du e OR u u + =
Background image of page 4
dx e . 1 -5x EXAMPLE: - dx e x . 2 4 x 3 ( 29 dx e e 3 - 2x . 3 x 6 x 2 2 + dx 2 e 3 . 4 x - dx e 3 e . 5 2 x x 2 dx 3xe . 6 3 1 3x - 2 dx x 5 . 7 2 2 1 2 x 1
Background image of page 5

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

View Full DocumentRight Arrow Icon
( 29 ( 29 du a ln a a d : call Re u u = ( 29 ( 29 ( 29 ( 29 ( 29 C a
Background image of page 6
Background image of page 7

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

View Full DocumentRight Arrow Icon
Background image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: a ln 1 du a a d a ln 1 du a a d du a a ln a d du a ln a side each of integral the Evaluate u u u u u u u u + = = = = ∫ ∫ ∫ ∫ ∫ ∫ ∫ C a ln a du a OR u u + = ∫ dx x 2 . 1 3 x 4 ∫ EXAMPLE: ∫ dx 7 x . 2 3 x 3 4 ( 29 dx 9 3 x 2 . 3 x 2 x 2 ∫ + EXERCISES: Evaluate the following integral. 3 1 x e dx-∫ dx e 1 x 2 ∫ 1 2 x e dx x-∫ ( 29 3 2 3 1 2 x x e dx e-∫ sin cos e d θ θ θ ∫ ∫ + + dx ) 1 x 2 ( 4 x 2 x 4 2 x x e dx e + ∫ ∫-+ 1 1 x x 2 dx e 1 e 4 1 x e dx x ∫ ∫ θ θ θ θ d e tan sec sec f....
View Full Document

This note was uploaded on 08/19/2011 for the course ECON 232 taught by Professor Charles during the Spring '11 term at MIT.

Page1 / 8

lesson 5 Integration of Exponential Function - a ln 1 du a...

This preview shows document pages 1 - 8. Sign up to view the full document.

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