MATH 1020U Lecture Notes - Lecture 1: Product Rule, Computer-Aided Technologies, Hebrew Language
Document Summary
Integration by parts (section 7. 1 of stewart; pg. Recall: so far, we have learned how to integrate some basic functions. Now we will continue to investigate more advanced integration techniques. Recall: you may remember that u-substitution came about based on undoing the chain rule. Similarly, we can use the product rule for differentiation to derive a useful rule for integration. The product rule states that, for f, g differentiable, xgxf xfxg xgxf d dx. Integration by parts formula: or, alternatively dxxgxf xgxf dxxgxf udv uv vdu. Integration by parts for definite integrals: b a xgxf dx xgxf b a b a xgxf dx. Now let"s go on to study some more complicated examples of applying integration by parts: Sometimes, you have to apply integration by parts more than once. Application: if the rate of change of medication in the bloodstream is to what is the net change in the amount of medication from time da dt.
