A calculus problem by Nazmus sakib

Calculus Level 3

Find the average value of x 2 + 1 x^2 + 1 in the interval [ 0 , 1 ] [0,1 ] .

1/3 3 4/3 2

Nazmus Sakib by Nazmus sakib , 24, Bangladesh

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1 solution

Chew-Seong Cheong
Apr 10, 2017

The average value is given by:

μ = ∫ 0 1 ( x 2 + 1 ) d x ∫ 0 1 d x = 1 3 x 3 + x ∣ 0 1 x ∣ 0 1 = 1 3 + 1 1 = 4 3 \begin{aligned} \mu & = \frac {\int_0^1 (x^2+1) \ dx}{\int_0^1 \ dx} = \frac {\frac 13x^3 + x \ \big|_0^1}{x \ \big|_0^1} = \frac {\frac 13 + 1}1 = \boxed{\frac 43} \end{aligned}

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