122
 
Integral calculus
 The indefinite integral
 Substitution rule

 Let f and g are differentiable, with range of g contained in the domain of f, and let F be antiderivative of  f  such that
 F' (u) = f(u) where u = g(x), then
     by applying the chain rule,      F(g (x))' = F' (g (x)) g' (x) = f (g (x)) g' (x) .
Thus, obtained is substitution rule
 Evaluating indefinite integrals using substitution rule examples
 Evaluate following indefinite integrals using substitution rule,
 Example:  Evaluate
 Solution:
 Example:  Evaluate
 Solution:
 Example:  Evaluate
 Solution:
 Example:  Evaluate
 Solution:
 Evaluate following indefinite integrals using substitution rule,
 Example:  Evaluate
 Solution:
 Example:  Evaluate
 Solution:
 Example:  Evaluate
 Solution:
 Example:  Evaluate
Solution:
 
 
 
 
 
 
 
Contents M
 
 
 
 
Copyright © 2004 - 2020, Nabla Ltd.  All rights reserved.