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Integration of polynomials
How do you find the anti-derivative using
the reverse of the power rule?
Methods (substitution,...
Remember the first way you
learned to derive
 F(x)=2x3
 F’(x)=2*3x(3-1)
 F’(x)=6x2
 The power rule derives a polynomia...
To integrate a polynomial you
do the reverse
Multiply coefficient by
exponent
Subtract one from the
exponent
Add one to th...
So to integrate 6x2 you
 Add one to the exponent of 2 giving you
x cubed
 And divide the coefficient, six, by the
new ex...
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Reverse power rule

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Reverse power rule

  1. 1. Integration of polynomials How do you find the anti-derivative using the reverse of the power rule? Methods (substitution, integraion by parts, integration by partial fractions) Word File with 2 ORIGINAL Examples of substitution(one must be trig)
  2. 2. Remember the first way you learned to derive  F(x)=2x3  F’(x)=2*3x(3-1)  F’(x)=6x2  The power rule derives a polynomial or variable by multiplying the variable’s coefficient by the exponent and subtracting one from the exponent
  3. 3. To integrate a polynomial you do the reverse Multiply coefficient by exponent Subtract one from the exponent Add one to the exponentDivide the coefficient by the NEW exponent
  4. 4. So to integrate 6x2 you  Add one to the exponent of 2 giving you x cubed  And divide the coefficient, six, by the new exponent three giving you:  2x3

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