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How do you evaluate the definite integral #int (1/x) dx# from #[1,2]#?

Answer 1

Elijah Abram

#ln2 ~= 0.69315#

#int_1^2 1/x dx = lnx]""_1^2# Standard integral

#= ln2-ln1 = ln2 -0#

#=ln2 ~= 0.69315#

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Answer 2

Adam Adkins

To evaluate the definite integral ( \int_{1}^{2} \frac{1}{x} , dx ), you can follow these steps:

Compute the antiderivative of ( \frac{1}{x} ), which is ( \ln|x| + C ).
Substitute the upper limit (2) into the antiderivative and subtract the result when the lower limit (1) is substituted.
Perform the subtraction to find the value of the definite integral.

[ \int_{1}^{2} \frac{1}{x} , dx = \ln|2| - \ln|1| ] [ = \ln(2) - \ln(1) ] [ = \ln(2) - 0 ] [ = \ln(2) ]

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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.