Find the average value of a function
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Find the average value of a function

[From: ] [author: ] [Date: 12-09-28] [Hit: ]
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I need to find the average value of the function f(x)=√(2x+1) ; [0,4]
The back of the book is saying the answer is 13/6 but i keep getting 4.333 (which is double the answer of the book). Can someone please help me I don't see where I'm going wrong and i want to understand how to do these problems.

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y_avg = (∫(from 0 to 4)(√(2x+1)dx))/(4-0)

∫√(2x+1)dx

Set u = √(2x+1)

u^2 = 2x + 1

2udu = 2dx

udu = dx

∫√(2x+1)dx = ∫u^2dx = (u^3)/3 = ((√(2x+1))^3)/3

Evaluate this from (0,4) we get 26/3

So y_avg = (26/3)/4 = 26/12 = 13/6
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