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svetlana [45]
3 years ago
7

Determine the interval on which f(x) = ln(x) is integrable.

Mathematics
2 answers:
Juliette [100K]3 years ago
8 0
<span>a. (0, ∞)
....................................</span>
PilotLPTM [1.2K]3 years ago
3 0
<h2>Answer:</h2>

  Option: a is the correct answer.

                  a.      (0, ∞)

<h2>Step-by-step explanation:</h2>

We are given a logarithmic function f(x) as:

f(x)=\ln x

We know that the logarithmic function is defined for all the real values strictly greater than 0 i.e. x>0.

i.e. the function is defined for all positive real numbers.

i.e. the domain of the function f(x) is: (0,∞).

Also, we know that the function f(x) is integrable in it's domain and the integration is calculated by using the integration by parts.

i.e.

\int\limits {\ln x} \, dx=\int\limits {1\cdot \ln x} \, dx\\  \\i.e.\\\\\int\limits {\ln x} \, dx=\ln x\cdot \int\limits {1} \, dx-\int\limits {\dfrac{d}{dx}\ln x} \cdot \int\limits {1} \, dx\\\\i.e.\\\\\int\limits {\ln x} \, dx=\ln x\cdot x-\int\limits {\dfrac{1}{x}\cdot x} \, dx\\\\i.e.\\\\\int\limits {\ln x} \, dx=x\cdot \ln x-\int\limits {1} \, dx\\\\i.e.\\\\\int\limits {\ln x} \, dx=x\cdot \ln x-x

Hence, the answer is: Option: a

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Step-by-step explanation:

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8 0
3 years ago
George wrote an integer. The opposite of George’s integer is -53. Which of these statements about George’s integer must be true?
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The George's integer must be true for option D)I and IV.

What is integer?

 A full number (not a fraction) that can be positive, negative, or zero is called an integer . -5, 1, 5, 8, 97, and 3, 043 are some examples of integers. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers. Integer, which means full or whole in Latin, is the root of the English term integer. A particular category of numbers called integers includes zero, positive numbers, and negative numbers. All whole numbers, both negative and positive, and 0 are considered integers.

Here the opposite of George integer is -53.

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George integer must be true for The given options I. the integer is 53 and IV.The integer has absolute value of 53.

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To learn more about integer refer the below link

brainly.com/question/13723636

#SPJ9

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Step-by-step explanation:

7 0
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