What is the average value of the function u ( x ) = 10 x sin &#x2061;<!-- ⁡ -->

Eden Solomon

Eden Solomon

Answered question

2022-06-08

What is the average value of the function u ( x ) = 10 x sin ( x 2 ) on the interval [ 0 , π ]?

Answer & Explanation

Quinn Everett

Quinn Everett

Beginner2022-06-09Added 23 answers

The average value is
1 π 0 0 π 10 x sin ( x 2 ) d x = 5 π 0 π 2 x sin ( x 2 ) d x
= 5 π [ cos ( x 2 ) ] 0 π
= 12 π
Pedantic Note
12 π π does NOT have a rational denominator.

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