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How do you evaluate the integral #int 1/x dx# from 0 to 1 if it converges?

Answer 1

Scarlett Allison

#int_0^1 1/xdx# diverges to #oo#

As #1/x->oo# as #x->0#, we must use an improper integral.

#int_0^1 1/xdx = lim_(M->0)int_M^1 1/xdx#

#=lim_(M->0)[ln(x)]_M^1#

#=lim_(M->0)(ln(1)-ln(M))#

#=lim_(M->0)-ln(M)#

#=oo#

Thus, the integral diverges to infinity.

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Answer 2

Ezra Adams

To evaluate the integral ∫(1/x) dx from 0 to 1, you need to determine if it converges. This integral represents the area under the curve y = 1/x from x = 0 to x = 1. Since the function 1/x has a vertical asymptote at x = 0, the integral diverges. Therefore, it does not converge.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.