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anonymous
 4 years ago
what is "In" in definite integral?
anonymous
 4 years ago
what is "In" in definite integral?

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0It's \[x \ln x x\] would you like me to prove it?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0well, xlnx  x evaluated between your two points

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0explain a little bit more plz..

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0can i send u a unsolved file ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Let'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 \[[ue^u]_{u= \ln a}^{u=\ln b}  \displaystyle\int_{\ln a}^{\ln b}e^udu\] \[= \left[(u1)e^u\right]_{u=\ln a}^{u=\ln b}\] \[=\left[(\ln x 1)x\right]_{x=a}^{x=b}\] \[=b(\ln b1)  a(\ln a 1)\] \[=\ln b^b  \ln a^a +(ab)\] \[=\ln \frac{b^b}{a^a} + a b\]
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