Find the average value of f(x)=cos(2x) on the interval [0,pi/2] .

pominjaneh6

pominjaneh6

Answered question

2022-08-05

Find the average value of f ( x ) = cos ( 2 x ) on the interval [ 0 , π / 2 ].

Answer & Explanation

Sanai Douglas

Sanai Douglas

Beginner2022-08-06Added 13 answers

f a v g = 1 π 2 0 0 π 2 f ( x ) d x
= 2 π 0 π 2 cos ( 2 x ) d x = 1 π sin ( 2 x ) | 0 π 2
= 1 π [ sin ( 2 π 2 ) sin ( 0 ) ] = 1 π [ 0 0 ] = 0

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