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Students explore methods for computing integrals of functions that are not in one of the standard forms.
In problem 1, students review both the chain rule for differentiation of composite functions and of the integrals of standard function form.
Students use substitution to integrate the square root of 2x + 3.
Students work through three problems using substitution to integrate. They first, discuss what they should use for u in each of the problems.
Students identify the common feature. They will see that each of the given functions in some way includes the derivative of the function substituted.
Students will learn to understand that this method will not work for all functions, but only certain well-chosen forms.
At the end of this activity, students will be able to compute an integral by u substitution.
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