Tough integration with unknown function

R

robrob

New member
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Aug 29, 2015
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2
Hi all,

I have some trouble identifying the steps that would lead to the following result:

I know that

0 = integral (from 0 to 2*theta^2) of [ g(x)*x^(2n-1) dx ]

g(s) being any real function of x

In the end the integration should lead that 0 = g(2*theta^2)*(2*theta^2)^(2n-1)*4*theta

Do anyone of you understand how to get to this result ? I tried integration by part, by substitution and I didn't manage to do it.
The explanation they provide is that they deviated both members wrt to theta.

Thanks in advance for your help !

Robrob
 
robrob said:
Hi all,

I have some trouble identifying the steps that would lead to the following result:

I know that

0 = integral (from 0 to 2*theta^2) of [ g(x)*x^(2n-1) dx ]

g(s) being any real function of x ......................................... check this for accuracy.

In the end the integration should lead that 0 = g(2*theta^2)*(2*theta^2)^(2n-1)*4*theta

Do anyone of you understand how to get to this result ? I tried integration by part, by substitution and I didn't manage to do it.
The explanation they provide is that they deviated both members wrt to theta.

Thanks in advance for your help !

Robrob
Click to expand...
.
 
robrob said:
Hi all,

I have some trouble identifying the steps that would lead to the following result:

I know that

0 = integral (from 0 to 2*theta^2) of [ g(x)*x^(2n-1) dx ]

g(s) being any real function of x

In the end the integration should lead that 0 = g(2*theta^2)*(2*theta^2)^(2n-1)*4*theta

Do anyone of you understand how to get to this result ? I tried integration by part, by substitution and I didn't manage to do it.
The explanation they provide is that they deviated both members wrt to theta.

Thanks in advance for your help !

Robrob
Click to expand...

Hint:
\(\displaystyle \frac{d}{dt}\int_0^{h(t)}\, f(x)\, dx\, = f(h(t)) h'(t)\)
 
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