SOLUTION: Please help me solve this equation: Prove the inequality without evaluating the integral. {{{ pi/12 <= int ( cos(x), dx, pi/6, pi/3 ) <= sqrt(3)pi/12 }}}

SOLUTION: Please help me solve this equation: Prove the inequality without evaluating the integral. {{{ pi/12 <= int ( cos(x), dx, pi/6, pi/3 ) <= sqrt(3)pi/12 }}}

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Question 345463: Please help me solve this equation: Prove the inequality without evaluating the integral.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
The value of the cosine function at the endpoints are,

The value of the function in between the endpoints is bounded by those values.

So then integrating,

Substituting,

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