calculo integral

calculo integral

1. antiderivatives (indefinite integrals)

   • notation: ∫f(x) dx =F(x)+c Where F(x) = the antiderivative of f(x) or v(t)dt= x(t) + c
     • properties
     • rules of sine and cosine square
     • rule 1
       • rule 2
     • basic rules of integration

2. differentiability

   • real change: ∆y= f(x+∆x) - f(x)
   • aproximate change: dy= f´(x)dx

3. Change of variable

   • example: ∫(2x+3)^7 u = 2x+3 du = 2dx du/2=dx (derivative) ∫u^7du/2 1/2∫ u^7 du =1/2(u^8/8) + c =1/16(2x+3)^8 + c
   • all the basic rules also apply to change of variable

4. velocity position

   • The more intervals you take, the more exact it is. Left hand or right hand calculations.
   • definite integral
     • area
       • area enclosed by 2 graphs
     • volume
     • properties of integrals

5. Partial Fractions

6. integration by parts

   • ∫udv= uv - ∫vdu
   • Election for U : 1.Logarithmic 2.Algebraic 3.Trigonometric 4.Exponential

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