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Integration of polynomials
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
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
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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Reverse power rule

  • 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. 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. 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