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Math Help - using Property of Integral to estimate the value

  1. #1
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    using Property of Integral to estimate the value

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  2. #2
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    racewithferrari,
    That is a good question.
    What have you done to solve it?
    I know you don't expect us to simlpy do it for you. Do you?
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  3. #3
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    I miss my class when teacher was teaching it. Other than that I learned how to solve integrals by myself from the book. But this thing confuses me.
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  4. #4
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    Well, the hardest part of this problem is determining m and M. However, we have an interval in which the function is non-increasing, [0,3]. So we know  f(3) \le f(x) \le f(0). From this we see that
     \frac{3}{1+3^2} \cdot (3 - 0)\le \int_0^3 \! \frac{3}{1 + x^2}\, dx \le \frac{3}{1+0^2} \cdot (3-0)
     \frac{9}{10}\le \int_0^3 \! \frac{3}{1 + x^2}\, dx \le 9
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  5. #5
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    can u actually tell me what will be in the two boxes

    thanks
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  6. #6
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    Quote Originally Posted by racewithferrari View Post
    can u actually tell me what will be in the two boxes
    I do not understand why you expect complete answers.
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  7. #7
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    Based on the way I did it, the boxes would be 9/10 and 9, respectively.
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