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Math Help - definite integral theorems!!

  1. #1
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    definite integral theorems!!

    Let the following be true.







    (b)



    (c)


    ok, everything i've tried for these seemed to be wrong, can someone show me how to do it, much thanks...haha

    mathlete
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by mathlete View Post
    Let the following be true.







    (b)



    (c)


    ok, everything i've tried for these seemed to be wrong, can someone show me how to do it, much thanks...haha

    mathlete
    Ok the first part is easy...well the first part of the first part is for the second part consider \bigg(\int_a^{b}f(x)\bigg)^2=\bigg(\int_a^{b}f(x)d  xdx\bigg)\cdot{\bigg(\int_a^{b}f(x)dx\bigg)}
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by mathlete View Post
    Let the following be true.







    (b)



    (c)


    ok, everything i've tried for these seemed to be wrong, can someone show me how to do it, much thanks...haha

    mathlete
    \int_a^b(4^2)dx-\left( \int_a^b f(x)dx \right)=16\int_a^bdx-\left( \int_a^b f(x)dx \right)^2 =16x|_a^b-(8)^2=16(b-a)-64

    Try the same thing on the 2nd.

    Good luck.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Mathstud28 View Post
    well the first part of the first part is for the second part consider
    huh?

    i think we are missing a period in there somewhere
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  5. #5
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Jhevon View Post
    huh?

    i think we are missing a period in there somewhere
    you are right...I meant to say....well. the. first. part. of. the. first part. is!......now that is an interesting and exciting sentence
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