Find the average value of the function over the given interval and all values of function equals its average values. f(x)=4x^3-3x^2,[-2,4]

pilinyir1

pilinyir1

Answered question

2022-09-20

Find the average value of the function over the given interval and all values of function equals its average values.
f ( x ) = 4 x 3 3 x 2 , [ 2 , 4 ]
Step1
Recall that the average value of a function over the given interval [a,b] is given by
1 b a a b f ( x ) d x

Answer & Explanation

ruinsraidy4

ruinsraidy4

Beginner2022-09-21Added 17 answers

Solution:
Average value = 1 b a a b f ( x ) d x
Here f ( x ) = 4 x 3 3 x 2 a = 2 ;   b = 4
= 1 4 2 2 4 ( 4 x 3 3 n 2 ) d x = 1 2 [ 4 x 4 4 3 x 3 3 ] 2 4 = 1 2 [ x 4 x 3 ] 2 4 = 1 2 × [ 4 4 4 3 2 4 + 2 3 ] = 92

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