How do you solve these integrals? help please!

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Answer 1 · 2018-05-30T02:41:54

See below.

a) We can rewrite as

$f(x) =x^-2$

$int f(x) dx = int x^-2 dx = -x^-1 + C$

b) This is simply $[-x^-1]_1^3 = -1/3 - (-1) = -1/3 + 1 = 2/3$

c) The integral can be rewritten as

$lim_(t-> oo) int_1^t x(1/x^2) dx$

$=lim_(t-> oo) int_1^t 1/x dx$

$=lim_(t-> oo) [lnx]_1^t$

$= ln(oo) - 0$

Since $ln(oo) = oo$ , this integral diverges therefore cannot be evlauated.

Hopefully this helps!