Solution to Finding the Integral of (x-4)/x^2 from 1 to 2

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Homework Help Overview

The discussion revolves around finding the integral of the function (x-4)/x^2 from 1 to 2, which falls under the subject area of calculus, specifically integral calculus.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the method of dividing the denominator and express uncertainty about the next steps after obtaining the expression 1/x - 4/x^2. Questions are raised about the integration of individual components and whether rewriting 1/x^2 as x^-2 is a valid approach.

Discussion Status

The discussion includes various attempts to clarify the integration process, with some participants offering guidance on integrating specific terms. There is no explicit consensus on a single method, but multiple interpretations and approaches are being explored.

Contextual Notes

Participants are navigating through the constraints of the problem, including the specific limits of integration and the expressions derived from the original function. There is an indication of differing levels of understanding regarding integration techniques.

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Homework Statement


Find the integral of (x-4)/x^2 dx from 1 to 2.


Homework Equations


Do I divide the denominator? I got 1/x-4/x^2 from 1 to 2. But what to do next?


The Attempt at a Solution


The answer is ln(2)-2.
 
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Nerd10 said:

Homework Statement


Find the integral of (x-4)/x^2 dx from 1 to 2.

Homework Equations


Do I divide the denominator? I got 1/x-4/x^2 from 1 to 2. But what to do next?

The Attempt at a Solution


The answer is ln(2)-2.

There are multiple methods to solve this integral, but the method you chose (dividing through by the denominator) is probably the easiest. The integral of two functions added together is the sum of the individual integrals of the functions: ##\int (f(x)+g(x))dx=\int f(x)dx+\int g(x)dx##
 
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Nerd10 said:
I got 1/x-4/x^2 from 1 to 2. But what to do next
Are you able to integrate 1/x^2 ? If so, then multiply the result by -4 and you'll have this problem half-solved.
 
Can it be 1/x^2=x^-2? And I integrate from there?
 
Never mind. I got it. Thanks for the help.
 

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