3.4a Definite Integral of f(x) from x=a to x=b


3.4a Definite Integral of f(x) from x=a to x=b


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


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


Leave a Comment