3.4 Definite Integrals Part 1

3.4 Definite Integrals (Part 1)


Example:
Evaluate each of the following.
(a)  1 0 ( 3 x 2 2x+5 )dx (b)  0 2 ( 2x+1 ) 3 dx

Solution:
(a)  1 0 ( 3 x 2 2x+5 )dx = [ 3 x 3 3 2 x 2 2 +5x ] 1 0 = [ x 3 x 2 +5x ] 1 0 =0[ ( 1 ) 3 ( 1 ) 2 +5( 1 ) ] =0( 115 ) =7 (b)  0 2 ( 2x+1 ) 3 dx = [ ( 2x+1 ) 4 4( 2 ) ] 0 2 = [ ( 2x+1 ) 4 8 ] 0 2 =[ ( 2( 2 )+1 ) 4 8 ][ ( 2( 0 )+1 ) 4 8 ] = 625 8 1 8 =78