Math Is Fun Forum

suetonius

Member

Registered: 2006-01-22

Posts: 1

anitderivative of 1/sqrt(x)

Can anybody help me find the antiderivative of 1/sqrt(x)?

irspow

Member

Registered: 2005-11-24

Posts: 1,055

Re: anitderivative of 1/sqrt(x)

The derivative of any fractional function:

f(x) = f(g)/f(h),  f'(x) = [ f'(g)f(h) - f(g)f'(h) ] / (f(h))²

In your case;

f(g) = 1,  f(h) = √x,  f'(g) = 0,  f'(h) = 1/(2√x)

So, using the formula for differentiating fractions above, this all becomes;

[ 0(√x) - 1(1/(2√x))] / (√x)²;

This equals;

-1/(2x√x) = (-1/2)x^(-3/2)

Note that this type of discussion belongs in the "HELP ME!" section.  Please post your math questions there in the future.

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I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

ryos

Member

Registered: 2005-08-04

Posts: 394

Re: anitderivative of 1/sqrt(x)

He was asking for the antiderivative, AKA the integral.

1/√x can be rewritten as ½x^-½. This can be integrated simply by the power rule for integration: ∫½x^-½dx = x^½ or √x.

Last edited by ryos (2006-01-22 13:01:30)

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El que pega primero pega dos veces.

irspow

Member

Registered: 2005-11-24

Posts: 1,055

Re: anitderivative of 1/sqrt(x)

Haha,  I guess that I was thrown off by this being posted in the wrong section.  It seems fitting that a wrong answer was given for a question posted in the wrong place.

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I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

justlookingforthemoment

Moderator

Registered: 2005-05-26

Posts: 2,161

Re: anitderivative of 1/sqrt(x)

Well, I was going to move it, but then I wasn't sure whether suetonius would be able to find it again.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: anitderivative of 1/sqrt(x)

Move it, but don't delete this thread, and place a "Thread moved to here: " link for this thread.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."