Question

Use Property 8 of the Integrals[m<=f(x)<=M, for a<=x<=b, than m(b-a)<=f(x)<=M(b-a)]to estimate the value of the integral:
integral tan(x)dx [(Pi/4, Pi/3)

Answer 1

I am confused on how to get my m and M values

Answer 2

do I just put Pi/4 and Pi/3 into the f(x)?

Answer 3

1<tanx<sq3
x]pi/4-pi/3<inttanx<sq3]pi/4-pi/3

Answer 4

so int belonging to (pi/12, pisq3/12)

Answer 5

So I put those two values back into the functions to get my low and high values and the just multiply each m, M by Pi\4-Pi\3?

Answer 6

exactly.

Answer 7

Thank you for your help!
Hopefully after I have done a few thousand or so of these integrals, they will become easier.