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Math Help - need to get the concept down...

  1. #1
    Junior Member winterwyrm's Avatar
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    need to get the concept down...

    Evaluate the integral.
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  2. #2
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    Okay I'm going to have to assume you know how to deal with expression in the form of \int_{}^{}{ae^{bx}}dx If you don't just say.

    Now to integrate 3^x we just need to rewrite it as e raised to an particular power, consider y = 3^x then ln(y) = ln(3^x) ....  ln(y) = xln(3) now we just antilog both sides so y = e^{xln3}

    so you understand how to write 3^x as e^{xln3}

    so to integrate you just use the chain rule backwards \int_{}^{}{e^{xln3}}dx = \frac{e^{xln3}}{ln3} = \frac{3^{x}}{ln3}

    now in general \int{a^x} dx = \frac{a^x}{lna}
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  3. #3
    Junior Member winterwyrm's Avatar
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    cool response, but it doesnt work.... F(3)-F(1) isnt' the right answer.....
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  4. #4
    Math Engineering Student
    Krizalid's Avatar
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    (a^x)'=(e^{x\ln a})'=a^x\ln a.

    Integrate both sides

    a^x+k_1=\int a^x\ln a\,dx\,\therefore\,\frac{a^x}{\ln a}+k=\int a^x\,dx.

    So \int_1^33^x\,dx=\left.\frac{3^x}{\ln3}\right|_1^3

    What's the problem with this?
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  5. #5
    Junior Member winterwyrm's Avatar
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    I get 21.84 when I plug that in, and when I try to submit it for my online homework..... I get a red X (I have a hundred submissions though)..... is this a serious problem?
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by winterwyrm View Post
    I get 21.84 when I plug that in, and when I try to submit it for my online homework..... I get a red X (I have a hundred submissions though)..... is this a serious problem?
    can't you enter exact answers? or does the system accept decimal approximations? (it would be 21.85 to two decimal places)
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  7. #7
    Junior Member winterwyrm's Avatar
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    its wrong... 22, 22.9, 21.85, even 21, and 23....
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by winterwyrm View Post
    its wrong... 22, 22.9, 21.85, even 21, and 23....
    check again to see if you wrote the right question, because i see nothing wrong with the responses given. did you try typing in 24/(ln 3)? this is definately the right answer for the question asked
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  9. #9
    Junior Member winterwyrm's Avatar
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    that worked! THanks so much!! I was so confused!!
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