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Marina86 [1]
2 years ago
6

Find the average value of the function over the given interval and all values of x in the interval for which the function equals

its average value. (Round your answer to three decimal places.) f(x) = 4x3 − 3x2, [−1, 3]
Mathematics
1 answer:
MrRissso [65]2 years ago
8 0

The average value of f(x)=4x^3-3x^2 over [-1, 3] is

\displaystyle\frac1{3-(-1)}\int_{-1}^3(4x^3-3x^2)\,\mathrm dx=\frac14\left(x^4-x^3\right)\bigg|_{-1}^3=\frac{(3^4-3^3)-(1+1)}4=\boxed{13}

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