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calc check: average value

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Find the average value of the function "f(x) = x^2 sqrt(1+x^3)" on the interval [0,2].

and this is what i did.. please check for mistakes. thanks :D

f(x) = x^2 sqrt(1+x^3), [0,2]
f ave = (1/(b-a))*inegral of a to b for: f(x) dx
f ave = (1/(2-0))*integral of 0 to 2 for: x^2 sqrt(1+x^3) dx
..let u = x^3 & du = 3x^2 dx
f ave = (1/2)*integral of 0 to 2 for: sqrt(1+u)*3 du
f ave = (3/2)*integral of 0 to 2 for: sqrt(1+u) du

= (3/2)[(2/3)(x+1)^(3/2)] from 0 to 2
= (3/2)[(2/3)((2)+1)^(3/2)] - (3/2)[(2/3)((0)+1)^(3/2)]
= (5.1962 - 1)
= 4.1962

When you change variables, you have to change limits of integration. When
x=0, u=0; when x=2, u=8

That will change the answer.

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