BigGlenntheHeavy
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\(\displaystyle Solve: \ \int_{0}^{ln(10)}\int_{e^{x}}^{10}\frac{1}{ln|y|}dy \ dx\)
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????
- Thread starter BigGlenntheHeavy
- Start date
I see what is going on.No need for all that complicated Exponential log stuff.
Use \(\displaystyle \frac{d}{dx}\int_{h(x)}^{g(x)}f(t)dt=f(g(x))g'(x)-f(h(x))h'(x)\) and you will get 9.
The fundamental theorem of calcarooney.
Use \(\displaystyle \frac{d}{dx}\int_{h(x)}^{g(x)}f(t)dt=f(g(x))g'(x)-f(h(x))h'(x)\) and you will get 9.
The fundamental theorem of calcarooney.
BigGlenntheHeavy
Senior Member
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- Mar 8, 2009
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- 1,577
\(\displaystyle galactus, \ you \ have \ to \ switch \ the \ order \ of \ integration, \ to \ wit:\)
\(\displaystyle \int_{0}^{ln(10)}\int_{e^{x}}^{10}\frac{1}{ln|y|}dy \ dx \ = \ \int_{1}^{10}\int_{0}^{ln|y|}\frac{1}{ln|y|}dx \ dy \ = \ 9.\)
\(\displaystyle Your \ answer \ is \ correct, \ usually \ people \ come \ up \ with \ the \ answer \ of \ 10.\)
\(\displaystyle Good \ show.\)
\(\displaystyle \int_{0}^{ln(10)}\int_{e^{x}}^{10}\frac{1}{ln|y|}dy \ dx \ = \ \int_{1}^{10}\int_{0}^{ln|y|}\frac{1}{ln|y|}dx \ dy \ = \ 9.\)
\(\displaystyle Your \ answer \ is \ correct, \ usually \ people \ come \ up \ with \ the \ answer \ of \ 10.\)
\(\displaystyle Good \ show.\)