AmTran_Bus
  • AmTran_Bus
Integrate
Mathematics
jamiebookeater
  • jamiebookeater
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AmTran_Bus
  • AmTran_Bus
|dw:1433471626709:dw|
zepdrix
  • zepdrix
Oo that's a fun problem :)
zepdrix
  • zepdrix
So what are we having trouble with, power rule on that first term ya?

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AmTran_Bus
  • AmTran_Bus
I just have no clue what to do.
zepdrix
  • zepdrix
\[\Large\rm \int\limits x^{\text{#}}dx=\frac{1}{\text{#+1}}x^{\text{#+1}}\]The exponent is just a number. We just apply our power rule for integration to that first term. e is just a fancy number.
zepdrix
  • zepdrix
\[\Large\rm \int\limits x^{3}dx=\frac{1}{4}x^{4}\]\[\Large\rm \int\limits x^e dx=\frac{1}{e+1}x^{e+1}\]
zepdrix
  • zepdrix
How bout the other term, integral of e^x?
AmTran_Bus
  • AmTran_Bus
Isn't it just e^x?
zepdrix
  • zepdrix
good good good.
zepdrix
  • zepdrix
\[\Large\rm \int\limits_0^1 x^e+e^x dx=\quad\frac{1}{e+1}x^{e+1}+e^x\quad |_0^1\]
zepdrix
  • zepdrix
So then just deal with the limits, ya? :d
AmTran_Bus
  • AmTran_Bus
I thought the integral of x^3 like you did above was x^4/4?
zepdrix
  • zepdrix
\[\Large\rm \frac{x^4}{4}=\frac{1}{4}x^4\]
AmTran_Bus
  • AmTran_Bus
Ok. Yes, I can apply the limits. I just wanted to get the core idea of the problem. Thanks.
zepdrix
  • zepdrix
no probs
zepdrix
  • zepdrix
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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