anonymous
  • anonymous
what is "In" in definite integral?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
It's \[x \ln x -x\] would you like me to prove it?
anonymous
  • anonymous
well, xlnx - x evaluated between your two points
anonymous
  • anonymous
explain a little bit more plz..

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anonymous
  • anonymous
can i send u a unsolved file ?
anonymous
  • anonymous
Let's prove it then... \[\displaystyle\int_{a}^{b}\ln x dx.\] Let u=lnx so that dx=xdu, x=e^u. Then our integral becomes \[\displaystyle\int_{\ln a}^{\ln b}ue^udu\] now use integration by parts \[[ue^u]_{u= \ln a}^{u=\ln b} - \displaystyle\int_{\ln a}^{\ln b}e^udu\] \[= \left[(u-1)e^u\right]_{u=\ln a}^{u=\ln b}\] \[=\left[(\ln x -1)x\right]_{x=a}^{x=b}\] \[=b(\ln b-1) - a(\ln a -1)\] \[=\ln b^b - \ln a^a +(a-b)\] \[=\ln \frac{b^b}{a^a} + a -b\]
anonymous
  • anonymous
I can't open it
anonymous
  • anonymous
why?

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