How Do You Integrate 4cos(n pi t)?

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Homework Help Overview

The discussion revolves around the integration of the function 4*cos(n pi t) with respect to t. Participants are exploring the correct approach to find the integral and are questioning their attempts and understanding of the integration process.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to determine the correct integral form and are comparing their results. Questions about the choice of substitution for integration and the differentiation of proposed solutions are raised.

Discussion Status

There is an ongoing exploration of different substitution methods for integration. Some participants are providing hints and prompting others to reconsider their choices, but there is no clear consensus on the correct approach yet.

Contextual Notes

There appears to be some confusion regarding the choice of variable for substitution and the differentiation of the proposed integrals. Participants are also navigating through the implications of their attempts without reaching a definitive conclusion.

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Homework Statement



integrate:
4*cos(n pi t) d(t)

Homework Equations


The Attempt at a Solution



is it: [4sin(n pi t)]/n.pi

or

[4t sin (n pi t)]/n.pi

any help very much welcome.
 
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What do you get if you differentiate those?

[itex]\int cos(u)du= sin(u)+ C[/edit]. What should you let u be? What is du?[/itex]
 
Last edited by a moderator:
HallsofIvy said:
What do you get if you differentiate those?

[itex]\int cos(u)du= sin(u)+ C[/itex]
[itex]. What should you let u be? What is du?[/QUOTE]<br /> <br /> Thanks for your quick reply, but you have lost me[/itex]
 
would u = 4

therefore du=0
 
Look at your given and the general solution:

[tex]\int 4cos(n\pi t) dt[/tex]

[tex]\int cos(u)du = sin(u)+ C[/tex]

Notice the similarity.
 

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