Integration

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Introduction to integration





LEARNING OUTCOMES

RESOURCES

  INTEGRATION 

 REVISE INTEGRATION

(35 LESSONS)  INTEGRATION JOKE!
 POLYNOMILAS & EXPONENTIALS  
 
Anti-differentiation

 INTEGRATE POLYNOMIAL
 
Negative/fractional powers


 NEGATIVE/FRACTIONAL POWERS
 
Evaluating C


 EVALUATING THE CONSTANT
 
Exponentials

 
INTREGRATE EXP JOKE!
 
1/x


INTEGRATING SIMPLE LOGARITHMIC
 TRIG FUNCTIONS  
 
Trig functions


 INTEGRATE TAN(2X)
 
Trig products

 
 
Chain rule

 
UNDOING CHAIN RULE
 
Quotients

 QUOTIENT RULE
 
Rational
 


 BY SUBSTITUTION  
 
Simple substitution

 SUBSTITUTION METHOD

COMMON ERRORS
 
Product substitution

 
SUSTITUTION INETGRAL 
 
EXTENSION EXERCISE 16,17,18



 DEFINITE INT & AREAS SOLIDS  
 
Evaluating integrals

 
Applications


 
Even/odd/periodic

 
 
Area above & below

 
Area between curves

 
Area with y-axis
(FROM MINUTE 2:30) 

Rotation around x-axis

 
Rotation around y-axis
 VOLUME AROUND Y-AXIS

SHELL METHOD

VOLUME ABOUT ANY AXIS
NUMERICAL INTEGRATION
 
Speradsheet

 
 
Trapezium rule

 TRAPEZIUM RULE
 
Simpson´s rule
 SIMPSON´S RULE 

EXTENSION 19,20,21,22
 

PROBLEM OF THE WEEK
 DIFFERENTIAL EQ´S  
 
Writing eq´s

 
 
Checking 1st order

 
 
Checking 2nd order
 
 
Solve simple dy/dx=f(x)
 
 
Separate variables
 
 
Particular solutions


 PARTICULAR SOLUTIONS
 
Solve differential eq´s
 
Newton´s cooling law
 
 
EXTENSION EXERCISE 23,24,25

 

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