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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: integrate plss !!
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[Post New]17 Feb 2008 16:35:34 IST
    Subject: integrate plss !!
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sweetgal17 (217)

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1. sin4x
(sin to the power 4 * x)
2.tan4x (tan to the power 4 * x .)
3.under root sin2x * cos2x !!
 
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[Post New]18 Feb 2008 11:55:50 IST
    Subject: Re:integrate plss !!
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joyfrancis (1504)

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sin4x
= (1-cos2x)2
= (1-((cos2x+1)/2))2
= (1+cos22x-2cos2x)/4
= (3+cos4x-4cos2x)/8
= 3x/8 - sin4x/32 + sin2x/4.......(ans)
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[Post New]18 Feb 2008 12:06:38 IST
    Subject: Re:integrate plss !!
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raulrag009 (1205)

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Q3
 
Let
I=?root(sin2xcos2x)
 
multiply and divide by root(2)
 
I = ?root(sin4x)/root(2)
 
Let
I1 = ?root(sin4x) dx
 
Put sin4x=t2
   4cos4xdx=2tdt
              dx=tdt/2root(1-t2)
 
I1 = ?t2dt/2root(1-t2)
 
I1 = (1/2) ? t2dt/root(1-t2)
 
NOw add and subtract by 1 in numerator
 
rest is easy
? is integral sign
Q2
 
? tan^4x
?tan^2xtan^2x
?(sec^2x-1)tan^2x
?sec^2xtan^2x  - ?tan^2x
put tanx=t        - ?sec^2x-1
?t^2dt       -  tanx  -x
t^3/3    - tanx-x +C
tan^3x/3 - tanx-x+C
  
 
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