Evaluate the definite integral

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Homework Help Overview

The problem involves evaluating a definite integral of the function sin(3t) with boundaries from 0 to π/3. The original poster expresses confusion regarding their initial attempt at the solution.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of substitution, specifically letting x = 3t, and question the implications for dt. There is an exploration of the integral of sin(x) and its relationship to the original integral.

Discussion Status

Participants are actively engaging with the problem, offering various approaches and clarifying misunderstandings about the substitution process. Some guidance has been provided regarding the integration of sine functions, and there is recognition of a mistake in the original poster's reasoning.

Contextual Notes

There is a noted confusion regarding the differential notation and the implications of the substitution made by the original poster. The discussion reflects a mix of correct and incorrect assumptions about integration techniques.

jimen113
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[SOLVED] Evaluate the definite integral

1. Homework Statement
[tex]\int[/tex] Sin(3t) dt; the boundaries are Pi/3 and zero.

Homework Equations





The Attempt at a Solution


3-cos(pi/3)[tex]^{}2[/tex]-cos(0)= not the correct answer.
Help!
 
Last edited:
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Do a substitution: x = 3t. if you do that, then what does dt = ?
Plug x in, what's the integral of sinx?
 
If x=3t, then
dt=3
integral of sin x is -cos x
Is this correct?
 
jimen113 said:
If x=3t, then
dt=3
integral of sin x is -cos x
Is this correct?
There is no substitution required (although that would yield the same answer).
Just look at the general integration formula for Sine:
[tex]\int\sin nx\dx=- \frac{\cos nx}{n} + \mbox{Constant}[/tex]
Can you get the answer now?
 
jimen113 said:
If x=3t, then
dt=3
integral of sin x is -cos x
Is this correct?

If x= 3t, then dx= 3dt so dt= (1/3)dx. "dt= 3" doesn't make any sense- a differential is not a number!
 
Thank you HallsofIvy, Reshma, & Izkelley for your help. I realized my mistake was: "dt=3"
 

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