Integration by Substitution
For continuous and with , : .
Proposition 4.26 (Integration by Substitution)
Let be continuous and let with , and , . Then
Proof
Let ; by the Fundamental Theorem of Calculus, Part 1, is well-defined and differentiable with . Set . By the chain rule, is differentiable:
Hence, applying the FTC to ,
Related
Stated in
- Proposition 4.26 (Integration by Substitution)§4.4 Integration and Differentiation