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cabellos6
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Homework Statement
the integral of 3/x
Homework Equations
The Attempt at a Solution
am i right in saying this is 3lnx
Tom Mattson said:And don't forget the absolute value bars. It's 3ln|x|+C.
Well, what do you think it is?rxtrejo said:Same question adding Limits of integration b=infinity a=0
Not so fast. This is an improper definite integral that requires limits at both endpoints to evaluate.NJunJie said:rxtrejo - you asking a question?
That would mean substituting the bounded values and find some 'area' within the limits you have given.
The integral of 3/x is ln|x| + C, where C is a constant of integration.
The domain of the integral of 3/x is all real numbers except 0, and the range is all real numbers.
To solve the integral of 3/x, you can use the power rule for integrals: ∫x^n dx = (x^(n+1))/(n+1) + C. In this case, n = -1, so the integral becomes (3x^-1)/(-1+1) + C = 3ln|x| + C.
Yes, the integral of 3/x can also be written as ln(1/x^3) + C or ln(1/(x^2)^3) + C.
The integral of 3/x can be interpreted as the area under the curve y = 3/x between the limits of integration. The value of the integral represents the net signed area between the curve and the x-axis.