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Integral Calculus

neeraj joshi's Avatar
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9 Oct 2009 13:10:40 IST
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kabi's Avatar

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Joined: 11 Jan 2009
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9 Oct 2009 17:09:11 IST
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2 . 1 / (1+cotx)

= sin(x) / ( cosx +sin(x))

= 1/ 2 ( 2 sin(x) / (sin(x) +cos(x))

= 1/2 ( sin(x)+cos(x) +sin(x) - cos(x)) / ( sinx +cosx)

=1/2 * ( 1 + (sinx-cosx)/(sinx+cosx))

integration = x/2  - log (sin(x) +cos(x)) /2

1 . Just resolve it .

Millind Gupta's Avatar

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10 Oct 2009 12:45:31 IST
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x5(x - 1)3 = x5 (x3 - 3x2+3x -1)   =   x8 - 3x7 +3x6 -x5

this can be integrted with respect to x with our simple knowledge of integrands and integrals

 

it is x9/9 -(3/8)x8 +(3/7)x7 - x6/6 +c

Priyak Dey's Avatar

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10 Oct 2009 14:44:53 IST
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In the first 1 u need to brk up the cubic term and integrate.......The second 1 is also damn easy............

Write cotx=cosx/sinx.....

So it becums-sinx/[sinx+cosx]...

in numerator write-[1/2][sinx+cosx-(cosx-sinx)]....

divide the two into two parts and u will get

1/2[sinx+cosx-ln|sinx+cos|.....Answer......

RATE IF USEFUL.....

Priyak Dey's Avatar

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Joined: 24 Sep 2009
Posts: 266
10 Oct 2009 14:47:32 IST
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In the first 1 u need to brk up the cubic term and integrate.......The second 1 is also damn easy............

Write cotx=cosx/sinx.....

So it becums-sinx/[sinx+cosx]...

in numerator write-[1/2][sinx+cosx-(cosx-sinx)]....

divide the two into two parts and u will get

1/2[sinx+cosx-ln|sinx+cos|.....Answer......

RATE IF USEFUL.....




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