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AmTran_Bus

  • one year ago

Integrate

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  1. AmTran_Bus
    • one year ago
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    |dw:1433471626709:dw|

  2. zepdrix
    • one year ago
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    Oo that's a fun problem :)

  3. zepdrix
    • one year ago
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    So what are we having trouble with, power rule on that first term ya?

  4. AmTran_Bus
    • one year ago
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    I just have no clue what to do.

  5. zepdrix
    • one year ago
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    \[\Large\rm \int\limits x^{\text{#}}dx=\frac{1}{\text{#+1}}x^{\text{#+1}}\]The exponent is just a number. We just apply our power rule for integration to that first term. e is just a fancy number.

  6. zepdrix
    • one year ago
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    \[\Large\rm \int\limits x^{3}dx=\frac{1}{4}x^{4}\]\[\Large\rm \int\limits x^e dx=\frac{1}{e+1}x^{e+1}\]

  7. zepdrix
    • one year ago
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    How bout the other term, integral of e^x?

  8. AmTran_Bus
    • one year ago
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    Isn't it just e^x?

  9. zepdrix
    • one year ago
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    good good good.

  10. zepdrix
    • one year ago
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    \[\Large\rm \int\limits_0^1 x^e+e^x dx=\quad\frac{1}{e+1}x^{e+1}+e^x\quad |_0^1\]

  11. zepdrix
    • one year ago
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    So then just deal with the limits, ya? :d

  12. AmTran_Bus
    • one year ago
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    I thought the integral of x^3 like you did above was x^4/4?

  13. zepdrix
    • one year ago
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    \[\Large\rm \frac{x^4}{4}=\frac{1}{4}x^4\]

  14. AmTran_Bus
    • one year ago
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    Ok. Yes, I can apply the limits. I just wanted to get the core idea of the problem. Thanks.

  15. zepdrix
    • one year ago
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    no probs

  16. zepdrix
    • one year ago
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    Yah you can rewrite your x term like that if you're more comfortable with it:\[\Large\rm \frac{1}{e+1}x^{e+1}=\frac{x^{e+1}}{e+1}\]

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