When working with composite functions, u-substitution often simplifies the integration process for us. What is sometimes overlooked, however, is the significant adjustment that occurs to the area beneath the curve. The image and link below allow students to explore the significance of this procedure.
Interactively explore u-substitution.
As seen below, u-substitution is not a viable approach to integration as its leads to division by zero. In the case below, and others like it, trigonometric substitution provides a means for us to move forward and solve many problems. The process below also brings trigonometric identities into play, thereby exposing students to their significance.
Thanks for reading.
samuelson mathxp 