lecture31hout

lecture31hout - MATH 006 Calculus and Linear Algebra...

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Unformatted text preview: MATH 006 Calculus and Linear Algebra (Lecture 31) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 11 Outline 1 Method of Substitution 2 Finding the Right Substitution 3 Examples Albert Ku (HKUST) MATH 006 2 / 11 Method of Substitution Method of Substitution Example Find each of the following indefinite integrals: (a) Z x 10 dx (b) Z (3 x + 2) 10 dx Solution (a) Z x 10 dx = x 11 11 + C (b) What is Z (3 x + 2) 10 dx ? The indefinite integral will be much simpler if (3 x + 2) can be replaced by a new variable u . This can be done by the method of subsitution . Albert Ku (HKUST) MATH 006 3 / 11 Method of Substitution The method of substitution is as follows: Let u be a new variable which is equal to an expression in x . In the example, we set u = 3 x + 2. Differentiate u with respect to x i.e. du dx = 3. Then we rewrite it formally as dx = 1 3 du Substitute 3 x + 2 by u and dx by 1 3 du in the indefinite integral. We get Z (3 x + 2) 10 dx = Z u 10 1 3 du = 1 3 Z u 10 du Albert Ku (HKUST) MATH 006 4 / 11 Method of Substitution...
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This note was uploaded on 12/28/2010 for the course MATH MATH006 taught by Professor Forgot during the Fall '09 term at HKUST.

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lecture31hout - MATH 006 Calculus and Linear Algebra...

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