( ) ( ) (a )   F x G x G b (b )  F or ( )dx (b ) (a )  f x G G where G is the primitive of f(x). a This is the Fundamental theorem of the Integral calculus. b 7.7 Evaluation of definite integrals Using the fundamental theorem of integral calculus we can evaluate definite integrals. The following examples will illustrate the evaluation of definite integrals. Example 1 3 dx Evaluate 2 2  x 2 Solution 2 3 3 2 3 8 4 3 1 20 = 18 – 3 66 34 Example 2 3 = xdx Evaluate 2 0 2 Solution  2 2 2 2 0 2 1 =  x 1
F ( x )  G ( x )  G (a ) or F (b )  b f ( x )dx  G (b ) G (a ) where G is the primitive of f(x). a This is the Fundamental theorem of the Integral calculus. b 7.7 Evaluation of definite integrals Using the fundamental theorem of integral calculus we can evaluate definite integrals. The following examples will illustrate the evaluation of definite integrals. Example 1 Evaluate 3 2 2  2 x dx Solution 3 2 2 3 3 8 3 4 1 = 18 – 20 3 66 Example 2 = 34 3 Evaluate 2 0 2 xdx Solution 2 2 2 0 2  1 2 1 = x 
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