Integral calculus
      Substitution and definite integration
         Substitution and definite integration examples
      Integrations by parts and the definite integral
Substitution and definite integration
When we evaluate an indefinite integral of the form
we use the substitutions  g (x) = u  and  g'(x) dx = du  to obtain
Therefore, to evaluate the definite integral using substitution
or
Note, by making substitution the definite integral change the limits of integration. That is, the new limits of integrations must correspond to the range of values for u as we now integrate the simpler integrand  f (u) from  ua = g (a)  to  ub = g (b).
Substitution and definite integration examples
Example:   Evaluate  
Solution: 
Example:   Evaluate
Solution: 
Integrations by parts and the definite integral
If u (x) and v (x) are continuous functions with continuous derivatives on [a, b], then
Example:   Evaluate
Solution: 
Functions contents G
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