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# Illustration a b c 3 illustration a b 4 illustrations

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Illustration: a) b) c) Subscribe to view the full document.

3. Illustration: a) b) 4. Illustrations: a) may be deleted may be deleted b) may be deleted Subscribe to view the full document.

BASIC THEOREMS OF INTEGRATION Let: u, v, w - are integrable functions of x 1. 2. 3. FUNDAMENTAL METHODS OF INTEGRATION I. THE POWER INTEGRAL: II. THE GENERAL POWER INTEGRAL: 1. 2. 3. 4. 5. SUMMARY: Subscribe to view the full document.

Exercises: Evaluate the following integrals. 1. 8. 2. 9. 3. 10. 4. 11. 5. 12. 6. 13. 7. (2x +3)dx 14. 1. 2. 3. 4. 5. Simple Substitution (General Power Formula) A technique called substitution , that can often be used to transform complicated integration problems into simpler ones. Quite often, the process of integration can be simplified by use of a substitution or change of variable. The purpose of substituting a new variable is to bring the problem to a form for which the standard formula, = + C n can be applied. Subscribe to view the full document.

Application: Integrate the following using u-substitution. 1. Solution. Let Substitute to the given, that lead to (Note: is known as integrating factor or correction factor) Apply general power formula Substitute back the value of u, the final answer is, 2. 3. Let u = Let u du = du = = = (Recall the law of exponents) = Subscribe to view the full document.

EXAMPLES: Find the indefinite integral. 1. 2. 3. 4. 5. • Summer '14

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