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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 begin the activity with a discussion and a review of both the chain rule for differentiation of composite functions and of the integrals of standard function forms.
Students make use of interactive MathBoxes that will guide them when they apply integration by substitution.
The function to be integrated is entered into f(x)= and then the choice of substitution into u=. They enter the derivative, du/dx into du=, and then substitute u*du.
They can then integrate with respect to u, and finally replace to give the result in terms of x. Each step is checked for algebraic equivalence.
Students work through several examples and identify a common feature when applying substitution by integration.
Students identify the common feature. They will see that each of the given functions in some way includes the derivative of the function substituted.
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