MAT136H1 Lecture : 5.5 Integration & Anti-derivatives Method of Substitution Question #2 (Medium)
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When evaluating the definite integral using the method of substitution, not only is the part of the function substituted by a simpler variable , but the original interval is also changed to match the substitution. So that, ( ( )) ( ) . Once the change of the interval is made from the start, substituting back in the original variable is not needed. This is the preferred and easier approach to solving definite integrals. Evaluate the definite integral using the method of substitution. Notice the functions in the numerator and the denominator. The key is to link these two in the form of. Chain rule, so that the most appropriate substitution is made. Thus, substituting the variables and , as well as the changed interval into the definite integral:
