Finding the Function and Constant in a Calculus Integration Problem

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Homework Help Overview

The problem involves finding a function f(x) and a constant a such that the equation 6 + integral f(t)/t^2 dt = 2x holds, with the limits of integration from a to x. This falls under the subject area of calculus, specifically integration and the application of the fundamental theorem of calculus.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the limits of integration and the form of the function f(t). There is an attempt to express f(t) in a way that facilitates solving the equation, with suggestions to differentiate to eliminate the integral.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and suggesting potential forms for f(t). Some guidance has been offered regarding the use of differentiation and the fundamental theorem of calculus, but no consensus has been reached.

Contextual Notes

There is a question regarding the limits of integration, which are confirmed to be from a to x. The original poster expresses uncertainty about the approach to the problem.

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Homework Statement



Find function f(x) and constant a such that,

6 + integral f(t)/t^2 dt = 2x limits of integral are a...x




Homework Equations


I am not quite sure how to approach this problem? What area of a calculus text would this type of problem be in?

Thanks in advance!


The Attempt at a Solution

 
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What are the limits of integration?
 
the limits are, a to x
 
if f(t) = 2 t^2, it seems you'll get the answer
 
You want to get f(t) out of the integral so you can solve for it, and to get rid of integrals you differentiate. You'll need to use the fundamental theorem of calculus.
 

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