Integration by substitution indefinite integral 5

Click For Summary

Homework Help Overview

The discussion revolves around the indefinite integral of the function involving \(5\pi \cos(\pi t)\). Participants are exploring the use of substitution methods in integration.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Some participants attempt to express the integral in terms of a substitution, suggesting \(u = \pi t\) and questioning the subsequent steps taken in the integration process. Others raise concerns about the clarity and connection between the expressions presented.

Discussion Status

The discussion is ongoing, with participants providing guidance on potential substitutions and questioning the relationships between different expressions. There is an active exploration of the integration process without a clear consensus on the steps taken.

Contextual Notes

Participants are working within the constraints of an indefinite integral and are navigating the complexities of substitution methods. There is a noted lack of clarity in the expressions used, which may affect the understanding of the problem.

char808
Messages
27
Reaction score
0

Homework Statement



indefinite integral 5\picos\pit

Homework Equations


The Attempt at a Solution



5\pi int cos\pit

Substitution Method

5\pi x sin (1/\pit
 
Physics news on Phys.org


char808 said:

Homework Statement



indefinite integral 5\picos\pit

Homework Equations





The Attempt at a Solution



5\pi int cos\pit

Substitution Method

5\pi x sin (1/\pit
Is this your integral?
\int 5 \pi cos(\pi t)dt
Click the integral above to see how the LaTeX looks.

A reasonable substitution would be u = \pi t, so du = \pi dt.
Can you take it from there?
 


<br /> 5 \pi sin(u)du<br /> <br />

<br /> <br /> 5 \pi sin(u) x du/ \pi<br /> <br />

<br /> <br /> 5sin(\pi t)<br /> <br />
 


What is the first line supposed to mean?
How did you get from the first line to the second?
How did you get from the second line to the third?
Are any of these expressions related to each other in any way?
Since this is an integration problem, one would think there should be an integral sign somewhere.
 

Similar threads

The indefinite integral and its "argument"
  • · Replies 3 ·
Replies
3
Views
2K
Finding an indefinite integral
  • · Replies 4 ·
Replies
4
Views
2K
Integral using substitution x = -u
  • · Replies 12 ·
Replies
12
Views
2K
Potential of a rotationally symmetric charge distribution
  • · Replies 4 ·
Replies
4
Views
2K
Find the result of definite integration
  • · Replies 6 ·
Replies
6
Views
2K
Integrate [cosec(30°+x)-cosec(60°+x)] dx in terms of tan x
  • · Replies 3 ·
Replies
3
Views
2K
Apparently impossible indefinite integral?
  • · Replies 22 ·
Replies
22
Views
2K
How can I solve this standard integral using substitution?
  • · Replies 6 ·
Replies
6
Views
2K
Solve Indefinite Integral: U Substitution
  • · Replies 2 ·
Replies
2
Views
2K
Can I Use Substitution to Prove the Residue Theorem Integral?
  • · Replies 5 ·
Replies
5
Views
2K