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Evaluate the definite integral

  • Thread starter jimen113
  • Start date
  • #1
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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:

Answers and Replies

  • #2
275
2
Do a substitution: x = 3t. if you do that, then what does dt = ?
Plug x in, whats the integral of sinx?
 
  • #3
67
0
If x=3t, then
dt=3
integral of sin x is -cos x
Is this correct?
 
  • #4
747
4
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?
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
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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!
 
  • #6
67
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Thank you HallsofIvy, Reshma, & Izkelley for your help. I realized my mistake was: "dt=3"
 

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