As you may notice,the variable is still hangingthere.To write it in termsof since solving
for we get, Substitutingbackinto the integral,
Applyingthe FundamentalTheoremof Calculusby insertingthe limitsof integrationand calculating,
Calculatingand simplifying,we get
We couldhavechosen instead.You may want to try to solvethe integralwith this substitution.
It mightbe easierand less tedious.
Example7:
Let’s try the substitutionmethodof definiteintegralswith a trigonometricintegrand.
Evaluate.
Solution:
Try Then
Lowerlimit: For
Upperlimit: For