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Integral Calculus

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2 Sep 2010 14:54:23 IST

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Integration

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If f(3x-4/3x+4)=x+2 then integral of f(x)dx = ?

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Vivek Agrawal

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Joined: 27 Jul 2009

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2 Sep 2010 16:24:57 IST

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first take inverse both sidethen replace x by f(x)-2u will get a linear eqn in the variable f(x)by solving it u will get exact value (or say machine) of f(x)then its preety simple to integrate using partial fractionsthis qustion came in cpt(narayana iit academy)

savita

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2 Sep 2010 18:15:11 IST

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can't we do it by the following method:

take 3x-4/3x+4 =y then express x in terms of y and then integrate f(y)dy

Yagyadutt Mishra

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5 Sep 2010 22:14:07 IST

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If f(3x-4/3x+4)=x+2 then integral of f(x)dx = ?

Take (3x - 4 )/( 3x + 4) = y

Then (3x - 4) / (3x +4) + 1 = y +1 (adding 1 both side )

6x/(3x + 4) = y + 1

(3x + 4) / 6x = 1 /( y + 1)

1/2 + 2/3x = 1/(y + 1)

2/3x = 1/(y+1) - 1/2

2/3x = (2 -y - 1)/(y+1)

2/3x = ( 1-y)/(y+1)

so x = 3(y+1)/2(1-y)

hence f(y) = 3(y+1)/2(y-1) + 2

f(y) = (3y + 3 + 4y - 4)/2(y-1)

f(y) = (7y -1 ) /2(y-1)

f(y) = (7y - 7 +6)/2(y-1)

f(y) = (7y-7) /2(y-1) + 3/(y-1)

f(y) = 7/2 + 3/(y-1)

intg(f(y)) = 7y/2 + 3.ln(y-2) + C

edison

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6 Sep 2010 16:26:21 IST

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You deserve a salute for this man !!!

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