(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\text {Find m such that }\displaystyle\int^m_4 \frac{1}{x\sqrt{x}}\,dx = .9[/tex]

2. Relevant equations

3. The attempt at a solution

[tex]\displaystyle\int^m_4 \frac{1}{x\sqrt{x}}\,dx = .9 \Rightarrow \displaystyle\int^m_4 x^{-3/2}\,dx = .9 \Rightarrow -2m^{-1/2} +2(4)^{-1/2} = .9 \Rightarrow m = \frac {4}{1.9^{2}} = 1.108[/tex]

If I plug this value back into the original integral, it comes out as [tex]-.9[/tex]. Should I solve this integral another way? Also, an extention of the problem is

[tex] \text {Explain why there is no number m such that} \displaystyle\int^m_4 \frac{1}{x\sqrt{x}}\,dx = 1.1[/tex]

It seems like that has to deal with convergence issues, something I'm just beginning to learn. Any hints for the first step?

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# Homework Help: Another method of solving integrals?

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