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Math Help - definite integrals

  1. #1
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    definite integrals

    1. how do I show that cos(x^2) is greater than or equal to cos(x) for 0 < x < 1?

    2. deduce that integral of cos(x^2)dx from 0 to pi/6 is greater than or equal to 1/2.
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  2. #2
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    Re: definite integrals

    Quote Originally Posted by Taurus3 View Post
    1. how do I show that cos(x^2) is greater than or equal to cos(x) for 0 < x < 1?

    2. deduce that integral of cos(x^2)dx from 0 to pi/6 is greater than or equal to 1/2.
    1) The \cos is a decreasing function on (0,1)~.
    If x\in (0,1) then x^2<x so \cos(x^2)>\cos(x)~.

    2) There is a theorem: If each of f~\&~g is integrable and \left( {\forall x \in [a,b]} \right)\left[ {f(x) \leqslant g(x)} \right] then \int_a^b f  \leqslant \int_a^b g .
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