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

Evaluate the definite integral.

2. Relevant equations

[tex]

\int_{1}^{2} ( 2e^{-4x} -\frac{1}{x^2} ) dx

[/tex]

Answer given by the book: [tex]\frac{1}{2}(e^{-4}-e^{-8}-1)[/tex]

3. The attempt at a solution

u = 4x; x = u/4; du = 4 dx; dx = du/4;

[tex]\frac{1}{2}\int e^{-u} du - 4\int u^{-2} du[/tex]

[tex]\frac{1}{2}\int_{1}^{2} e^{-4x} dx - 4\int_{1}^{2} \frac{1}{16x^2} dx[/tex]

... and I continue down this path to wind up with:

[tex] \frac{1}{2e^8}-\frac{1}{2e^4}-\frac{21}{32}[/tex]

In other words, I've apparently no idea what I'm doing, and would appreciate any help.

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# Homework Help: Definite integral

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