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How do you compute the value of #int 1/x dx# of #[1,10]#?

Answer 1

Paisley Johnson

Using the fundamental theorem of Calculus

#int_a^b f(x)dx = F(b) - F(a)# where #(dF(x))/dx = f(x)#

As:

#int_1^"10"1/x dx = int_1^"10" d((ln(x)))/dx = ln(x) |_1^"10"= ln(10) -ln(1) = ln(10)#

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Answer 2

Christopher Agresta

To compute the value of ∫(1/x) dx from 1 to 10, you would evaluate the integral of 1/x with respect to x over the interval [1, 10]. The integral of 1/x is ln|x|, where ln represents the natural logarithm function. Therefore, you would integrate ln|x| from 1 to 10 and then evaluate the result. The integral of ln|x| from 1 to 10 is ln(10) - ln(1), which simplifies to ln(10). Therefore, the value of the integral ∫(1/x) dx from 1 to 10 is ln(10).

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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.