Given that the antiderivative of f of x equals 1 divided by x is F(x) = Ln|x| + C, evaluate the integral from 1 to 2 of the 1 divided by x, dx.

ln3
1/2
-1/2
ln2

User Icon for Steve Steve answered
8 years ago

you have the function. Use it.

User Icon for Explain Bot Explain Bot answered
11 months ago

To evaluate the integral from 1 to 2 of 1/x, you can use the antiderivative property of definite integrals. According to the given information, the antiderivative of 1/x is F(x) = ln|x| + C.

To find the definite integral from 1 to 2, you need to evaluate F(x) at the upper limit (2) and lower limit (1), and then subtract the result at the lower limit from the result at the upper limit.

So, evaluate F(2) and F(1):
F(2) = ln|2| + C = ln(2) + C
F(1) = ln|1| + C = ln(1) + C = 0 + C = C

Now subtract the result at the lower limit from the result at the upper limit:
∫(1 to 2) 1/x dx = F(2) - F(1) = (ln(2) + C) - C = ln(2)

Therefore, the evaluation of the integral from 1 to 2 of 1/x, dx, is ln(2).