The average value of the function u(x) = 10x sin(x²) on the interval [0, √π/2] is calculated using the integral of the function. The integral yields -5cos(x²), and substituting the limits 0 and √π/2 results in a value of 10. The final average value is determined by multiplying this result by 1/(b-a), leading to the conclusion that the average value is 10/√π.
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[ itex ]\sqrt{\pi}[ /itex ] - omit the extra spaces.8point1 said:Homework Statement
Find the average value of the function u(x)= 10xsin(x2) on the interval [0, ∏1/2]
(Sorry, I can't figure out how to make the square root symbol)
I get the same thing. Good work!8point1 said:Homework Equations
The Attempt at a Solution
For the integral of u(x), I got -5cos(x2)
I substituted 0 and ∏1/2 and got 10.
then I multiplied by 1/b-a which was 1/∏1/2
making my final answer 10/∏1/2