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 }}}

Algebra ->  Test -> 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 }}}      Log On


   



Question 345463: Please help me solve this equation: Prove the inequality without evaluating the integral. +pi%2F12+%3C=+int+%28+cos%28x%29%2C+dx%2C+pi%2F6%2C+pi%2F3+%29+%3C=+sqrt%283%29pi%2F12+
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The value of the cosine function at the endpoints are,
cos%28pi%2F6%29=sqrt%283%29%2F2
cos%28pi%2F3%29=1%2F2
The value of the function in between the endpoints is bounded by those values.
1%2F2%3C=cos%28x%29%3C=sqrt%283%29%2F2
So then integrating,


pi%2F3-pi%2F6=%282pi%29%2F6-pi%2F6=pi%2F6
Substituting,