Integration problem

  • Thread starter tunabeast
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  • #1
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Homework Statement


Compute the following antiderivative [tex] \int (sin^3(x))(cos^4(x)) dx [/tex]


Homework Equations





The Attempt at a Solution


If this problem requires use of integration by parts i'm struggling to work out to split it up and make it manageable. Have searched countlessly for a similar example on the net but have had no luck. Thanks
 

Answers and Replies

  • #2
HallsofIvy
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There is a standard "method" when you have a trig function to an odd power.

Since sin(x) it to the 3rd power, take one out to use with dx, convert sin2(x) to cos:
[tex]\int sin^3(x)cos^4(x)dx= \int sin^2(x)cos^4(x) sin(x)dx= \int (1- cos^2(x))cos^4(x) sin(x)dx[/itex]
Now what substitution will make that easy?
 
  • #3
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All you should do is new variable u = cos(x). You'll get integral u^4-u^6.
 
  • #4
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Actually, [tex]u^6 - u^4[/tex] due to the negative in the derivative of [tex]cos(x)[/tex]
 
Last edited:
  • #5
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fikus what do you mean, i can do a substitution straight away?
 
  • #6
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fikus what do you mean, i can do a substitution straight away?
you can once you find that the derivative of your substitution appears in your original problem
 
  • #7
HallsofIvy
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fikus what do you mean, i can do a substitution straight away?
I believe that is what everyone as been trying to tell you!
 

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