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!