How do you find the average value of f(x)=-x^4+2x^2+4f(x)=−x4+2x2+4 as x varies between [-2,1][−2,1]?

1 Answer
Jim G.
Dec 6, 2016

121/1512115

Explanation:

Since f(x) is continuous on the closed interval [-2 ,1] the average value is.

color(red)(bar(ul(|color(white)(2/2)color(black)(1/(b-a)int_a^bf(x)dx)color(white)(2/2)|)))
where [a ,b] is the closed interval.

rArr1/(1+2)int_-2^1(-x^4+2x^2+4)dx

=1/3[-1/5x^5+2/3x^3+4x]_-2^1

1/3[(-1/5+2/3+4)-(-32/5-16/3-8)]

=1/3[67/15-(-296/15)]=1/3(363/15)=121/15

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