How do you evaluate the integral $int 2/x^5 dx$ from $-oo$ to $-1$ ?

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Answer 1 · 2016-08-01T17:46:55

$int_(-oo)^(-1)2/x^5dx=-1/2$

We have:

$int_(-oo)^(-1)2/x^5dx=2int_(-oo)^(-1)x^-5dx$

Evaluating the integral:

$=2[x^(-4)/(-4)]_(-oo)^(-1)$

$=-1/2[1/x^4]_(-oo)^(-1)$

$=-1/2[1/(-1)^4-lim_(xrarr-oo)1/x^4]$

$=-1/2[1/1-0]$

$=-1/2$

How do you evaluate the integral int 2/x^5 dxint 2/x^5 dx from -oo-oo to -1-1?