An integration problem which is supposed to be easy

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Homework Help Overview

The discussion revolves around an integration problem that the original poster finds challenging. The subject area is calculus, specifically focusing on techniques of integration and the application of the fundamental theorem of calculus.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts various integration techniques, including the fundamental theorem of calculus, substitution, and integration by parts, but expresses confusion about their application. Some participants suggest using the Leibniz integral rule and changing the integration variable to simplify the problem. There is also a discussion about relating the integral to the expression 1-cos(x).

Discussion Status

The discussion is active, with participants offering different approaches and suggestions. While some guidance has been provided regarding variable substitution and differentiation, there is no explicit consensus on the best method to proceed.

Contextual Notes

Participants are navigating through various assumptions about the integral's setup and the relationships between the functions involved. The original poster's uncertainty about the effectiveness of their chosen methods is evident.

kyva1929
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I am just lost at how to use the given information to find out the required integral. I've tried fundamental theorem of calculus, substitution, and integration by parts, but they do not seem to work for me.

Thank you!
 
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Sure. Use the fundamental theorem in the form of the Liebniz integral rule. Then look for something to integrate by parts.
 
Actually, I think it's even easier if you change the integration variable to u=x-t. THEN apply the fundamental theorem.
 
Dick said:
Actually, I think it's even easier if you change the integration variable to u=x-t. THEN apply the fundamental theorem.

Using u=x-t, du=-dt, and the integral becomes -(x-u)*f(u) du integrating from x to 0, but now I am not sure how it could be integrated to some useful form relating it to 1-cos(x) ?
 
Your u integral is equal to 1-cos(x). Now differentiate both sides.
 
Dick said:
Your u integral is equal to 1-cos(x). Now differentiate both sides.

I got it, thank you very much!
 

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