12 x1 t01 03 integrating derivative on function (2013)
Upcoming SlideShare
Loading in...5
×
 

12 x1 t01 03 integrating derivative on function (2013)

on

  • 813 views

 

Statistics

Views

Total Views
813
Slideshare-icon Views on SlideShare
563
Embed Views
250

Actions

Likes
1
Downloads
18
Comments
0

1 Embed 250

http://virtualb15.edublogs.org 250

Accessibility

Categories

Upload Details

Uploaded via as Adobe PDF

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

    12 x1 t01 03 integrating derivative on function (2013) 12 x1 t01 03 integrating derivative on function (2013) Presentation Transcript

    • Integrating Derivative on Function
    • Integrating Derivative on Function  f  x  dx  log f  x   c f x
    • Integrating Derivative on Function  e.g. (i) 1  7  3x dx f  x  dx  log f  x   c f x
    • Integrating Derivative on Function  e.g. (i) 1  7  3x dx 1 3   dx 3 7  3x f  x  dx  log f  x   c f x
    • Integrating Derivative on Function  e.g. (i) f  x  dx  log f  x   c f x 1  7  3x dx 1 3   dx 3 7  3x 1   log7  3 x   c 3
    • Integrating Derivative on Function  e.g. (i) f  x  dx  log f  x   c f x 1  7  3x dx 1 3   dx 3 7  3x 1   log7  3 x   c 3 ii  dx  8x  5
    • Integrating Derivative on Function  e.g. (i) f  x  dx  log f  x   c f x 1  7  3x dx 1 3   dx 3 7  3x 1   log7  3 x   c 3 dx  8x  5 1 8dx   8 8x  5 ii 
    • Integrating Derivative on Function  e.g. (i) f  x  dx  log f  x   c f x 1  7  3x dx 1 3   dx 3 7  3x 1   log7  3 x   c 3 dx  8x  5 1 8dx   8 8x  5 1  log8 x  5  c 8 ii 
    • Integrating Derivative on Function  f  x  dx  log f  x   c f x e.g. (i)  1 dx 7  3x 1 3   dx 3 7  3x 1   log7  3 x   c 3 dx ii   8x  5 1 8dx   8 8x  5 1  log8 x  5  c 8 x5 iii   6 dx x 2
    • Integrating Derivative on Function  f  x  dx  log f  x   c f x e.g. (i)  1 dx 7  3x 1 3   dx 3 7  3x 1   log7  3 x   c 3 dx ii   8x  5 1 8dx   8 8x  5 1  log8 x  5  c 8 x5 iii   6 dx x 2 1 6 x5   6 dx 6 x 2
    • Integrating Derivative on Function  f  x  dx  log f  x   c f x e.g. (i)  1 dx 7  3x 1 3   dx 3 7  3x 1   log7  3 x   c 3 dx ii   8x  5 1 8dx   8 8x  5 1  log8 x  5  c 8 x5 iii   6 dx x 2 1 6 x5   6 dx 6 x 2 1  logx 6  2   c 6
    • 1 iv   dx 5x
    • 1 iv   dx 5x 1 5   dx 5 5x
    • 1 iv   dx 5x 1 5   dx 5 5x 1  log 5 x  c 5
    • 1 iv   dx 5x 1 5   dx 5 5x 1  log 5 x  c 5 OR 1 1  x dx 5
    • 1 iv   dx 5x 1 5   dx 5 5x 1  log 5 x  c 5 OR 1 1  x dx 5 1  log x  c 5
    • 1 iv   dx 5x 1 5   dx 5 5x 1  log 5 x  c 5 4x 1 v   dx 2x 1 OR 1 1  x dx 5 1  log x  c 5
    • 1 iv   dx 5x 1 5   dx 5 5x 1  log 5 x  c 5 4x 1 v   dx 2x 1 OR 1 1  x dx 5 1  log x  c 5 order numerator  order denominator
    • 1 iv   dx 5x 1 5   dx 5 5x 1  log 5 x  c 5 4x 1 v   dx 2x 1 OR 1 1  x dx 5 1  log x  c 5 order numerator  order denominator  polynomial division
    • 1 iv   dx 5x 1 5   dx 5 5x 1  log 5 x  c 5 4x 1 v   dx 2x 1 OR 1 1  x dx 5 1  log x  c 5 order numerator  order denominator  polynomial division 2 2x 1 4x 1 4x  2 1
    • 1 iv   dx 5x 1 5   dx 5 5x 1  log 5 x  c 5 4x 1 dx v   2x 1 2  1  dx     2 x  1 OR 1 1  x dx 5 1  log x  c 5 order numerator  order denominator  polynomial division 2 2x 1 4x 1 4x  2 1
    • 1 iv   dx 5x 1 5   dx 5 5x 1  log 5 x  c 5 OR 1 1  x dx 5 1  log x  c 5 order numerator  order denominator 4x 1 dx v    polynomial division 2x 1 2  1  dx 2   2x 1 4x 1   2 x  1 1 4x  2  2 x  log2 x  1  c 2 1
    • vi  2 2x  x 2  1dx 1
    • vi  2 2x  x 2  1dx 1  logx  11 2 2
    • vi  2 2x  x 2  1dx 1  logx  11 2 2  log 5  log 2
    • vi  2 2x  x 2  1dx 1  logx  11 2 2  log 5  log 2 5  log  2
    • vi  2 vii  Differentiate x 3 log x and hence 2x  x 2  1dx 1  logx  11 2 2  log 5  log 2 5  log  2 integrate x 2 log x
    • vi  2 vii  Differentiate x 3 log x and hence 2x  x 2  1dx 1  logx  11 2 2  log 5  log 2 5  log  2 integrate x 2 log x d 3 3 1 x log x  x    log x 3x 2  dx  x
    • vi  2 vii  Differentiate x 3 log x and hence 2x  x 2  1dx 1  logx  11 2 2  log 5  log 2 5  log  2 integrate x 2 log x d 3 3 1 x log x  x    log x 3x 2  dx  x  x 2  3 x 2 log x
    • vi  2 vii  Differentiate x 3 log x and hence 2x  x 2  1dx 1  logx  11 2 2  log 5  log 2 5  log  2 integrate x 2 log x d 3 3 1 x log x  x    log x 3x 2  dx  x  x 2  3 x 2 log x  x 2  3 x 2 log x dx  x 3 log x  c
    • vi  2 vii  Differentiate x 3 log x and hence 2x  x 2  1dx 1  logx  11 2 2  log 5  log 2 5  log  2 integrate x 2 log x d 3 3 1 x log x  x    log x 3x 2  dx  x  x 2  3 x 2 log x  x 2  3 x 2 log x dx  x 3 log x  c 3 x 2 log xdx  x 3 log x   x 2 dx  c
    • vi  2 vii  Differentiate x 3 log x and hence 2x  x 2  1dx 1  logx  11 2 2  log 5  log 2 5  log  2 integrate x 2 log x d 3 3 1 x log x  x    log x 3x 2  dx  x  x 2  3 x 2 log x  x 2  3 x 2 log x dx  x 3 log x  c 3 x 2 log xdx  x 3 log x   x 2 dx  c 1 3 1 3  x log xdx  3 x log x  9 x  c 2
    • vi  2 vii  Differentiate x 3 log x and hence 2x  x 2  1dx 1  logx  11 2 2  log 5  log 2 5  log  2 integrate x 2 log x d 3 3 1 x log x  x    log x 3x 2  dx  x  x 2  3 x 2 log x  x 2  3 x 2 log x dx  x 3 log x  c 3 x 2 log xdx  x 3 log x   x 2 dx  c 1 3 1 3  x log xdx  3 x log x  9 x  c 2 Exercise 12D; 1 to 12 ace in all, 14a* Exercise 12E; 1 to 6 all, 7 to 21 odds, 22abc*, 23*