The mean value of the function $$f(x)=2ex+1$$ on the interval [$$0$$, $$2$$] is

Correct option is 32+log⁡2e2+1

Questions

The mean value of the function $f (x) = \frac{2}{e^{x} + 1}$ on the interval [0, 2] is

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log⁡2e2+1

1+log⁡2e2+1

2+log⁡2e2+1

2+log⁡e2+1

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detailed solution

Correct option is C

Average = 12∫02 2ex+1dx=∫02 e−x1+e−xdx=−log⁡1+e−x02=log⁡2−log⁡1+e−2=2+log⁡2/1+e2

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The mean value of the function f(x)=2ex+1 on the interval [0, 2] is

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The mean value of the function $f (x) = \frac{2}{e^{x} + 1}$ on the interval [0, 2] is