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Tables of Integrals and Computer Software for Integrals (9/19/08) Because finding antiderivatives is often a tricky and time-consuming job, – Tables of integrals are available (e.g., in the back of our textbook) which may be of use, and – Computer software exists (e.g., Mathematica) which can do quite a few antiderivatives. As “students of calculus” we can use these, but we also should have some idea how these tables and software were developed.

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Example What is ? Try to find a “form” in the table which fits this. What number is it? What’s the answer? What’s Mathematica say?

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Another Example What is ? Try to find a “form” in the table which fits this. What number is it? What’s the answer? What’s Mathematica say?

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And One More What is ? Try to find a “form” in the table which fits this. What number is it? What’s the answer? What’s Mathematica say?

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All Might Fail! The fact is that there are many elementary functions for which no elementary antiderivative is known to exist. In fact, in some sense, “most” functions can’t be anti-differentiated! (Contrast with derivatives.) To find definite integrals of such functions, we turn to numerical (approximate) integration.

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Assignment Hand-in #1 is due next Thursday, Sept 25 at 4:45 pm. Monday we will have Lab #2. You must bring your text (the Table of Integrals) to this lab. For Wednesday, please read Section 7.6 and do Exercises 5-15 odd. If you want, also check your answers with Mathematica.

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