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posted by  Vincenzo on 11/28/2008 7:31:56 PM  |  status: Live  

Integrating trig function!

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using
a. a trig identity
b. Integration by parts
Tags: Calculus
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Oracle
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posted by Bpanda on 11/28/2008 7:38:10 PM  |  status: Live
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Vincenzo's comment:
"thanks"
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we know that :
 
and
 
 
therefore : 
 
then  :   
 
the integral becomes:   
 
 
 
where C is a constant of integration
 
hope this helps
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posted by roydesoto on 11/28/2008 7:45:50 PM  |  status: Live
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identity:



for parts [which the above poster omitted], let u = sin θ and dv = sin θ dθ so du = cos θ dθ and v = -cos θ dθ:



[ignore all the boxes -- something got messed up during editing]

now add the remaining integral on the right to both sides to get:



and divide by 2 to get the answer


now
Oracle
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posted by Bpanda on 11/28/2008 7:52:21 PM  |  status: Live
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Vincenzo's comment:
"thanks!!!!!!!!!!!!!!!!!!!!!"
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2) by using integration by parts
 
u = sinθ
du = cosθ .dθ 
dv = sinθ.dθ
v = -cosθ
 
the integral becomes: 
 
 
we know that :   
 
therefore : 
 
====> 
 
finally : 
 
hope this helps
 
You Don't Mess with the Panda
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posted by A-Rod 7821 on 11/28/2008 8:17:07 PM  |  status: Live
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Vincenzo's comment:
"thanks!!!!!!!!!!!!!!!"
Response Details:
Use the power reduction formula:
Use U-Substitution let u=2θ
du=2dθ
du/(2)=dθ
---(ANSWER)---
 
(B) Integration By Parts
Formula:
 
 
 
 
 
 
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