calculus

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It is known that if m <= f(x) <= M for a <= x <= b, then the following property of integrals is true.

m(b-a) <= int_a^b f(x)dx <= M(b-a)

Use this property to estimate the value of the given integral.

? <= int_0^3 3/(1+x^2)dx 2 <= ?

solve for the ?

  • calculus -

    ? <= int_0^3 3/(1+x^2)dx 2 <= ?

    I do not know what that last 2 is about
    I assume you mean integral from 0 to 3 of
    3 dx /(1+x^2)
    well if x were 0 the whole way we would have a bigger result
    3(3-0) = 9
    and if x were 3 the whole way we would have a small result
    3 (3/10 - 0) = .9

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