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