Find the average value f a v e of the function f on the given...

NormmodulxEE

NormmodulxEE

Answered

2022-12-03

Find the average value f a v e of the function f on the given interval.
f ( x ) = 3 x 2 + 8 x , [ 1 , 2 ]

Answer & Explanation

revessatrP6

revessatrP6

Expert

2022-12-04Added 11 answers

f ( x ) = 3 x 2 + 8 x , [ 1 , 2 ]
Average value of f ( x ) = 1 b a a b f ( x ) d x = 1 2 ( 1 ) 1 2 ( 3 x 2 + 8 x ) d x = 1 3 [ 3 x 3 3 + 8 x 2 2 ] 1 2 = 1 3 ( x 3 + 4 x 2 ) 1 2 = 1 3 [ 2 3 + 4 × 2 2 ( ( 1 ) 3 + 4 × ( 1 ) 2 ) ] = 1 3 [ 8 + 16 ( ( 1 ) + 4 ) ] = 1 3 [ 24 3 ] = 1 3 × 21 = 7

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