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7.6 Evaluation of Definite Integral

The numerous techniques that can be used to evaluate indefinite integrals, can be used to evaluate definite integrals. Integration by substitution and change of variable, integration by parts and integration by partial fractions are these techniques.

(I) Substitution and Change of Variables

Example 17 Evaluate

Solution : Let I =

Put x2 + 1 = t, then 2x dx = dt

\ x dx = dt / 2

The limits of integration can be converted from x to their corresponding t values as

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7.1 Definition
7.2 Definite integral as on an area under curve
7.3 Working rule for evaluation of a definite integral as a limit of a sun
7.4 Fundamental theorem of integrated calculus
7.5 Properties of definite integrals
7.6 Evaluation of definite integral
7.7 Reduction formulas

Chapter 8

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