f-x-3x-2-6x-1-5-find-the-average-value-

Question Number 135361 by leena12345 last updated on 12/Mar/21

f (x) = 3 x^{2} + 6 x, [- 1, 5]

f i n d - t h e - a v e r a g e - v a l u e

Answered by mr W last updated on 12/Mar/21

a v e r a g e o f f (x) o v e r [a, b] :

f_{m} = \frac{\int_{a}^{b} f (x) d x}{b - a} = \frac{\int_{- 1}^{5} (3 x^{2} + 6 x) d x}{5 - (- 1)}

= \frac{{[x^{3} + 3 x^{2}]}_{- 1}^{5}}{6} = \frac{5^{3} + 3 \times 5^{2} - {(- 1)}^{3} - 3 {(- 1)}^{2}}{6}

= \frac{198}{6} = 33

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