Question

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 ?

Answer 1

? <= 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