# Calculate between [-epsilon,epsilon]

i need to integrate

$$-(p(y)f(y)')'=m^2w(y)f(y)$$
where
$$p(y)=e^{4ky}(1-4ak^2)$$ and $$w=-4ae^{2y}k\delta(y)$$

but y between [0,infinity[

¿i calculate between $$\int^{epsilon}_0????$$ or ¿i calculate between [-epsilon,epsilon]?????

but, what is??

$$\int^{\epsilon}_0(p(y)f(y)')'dy$$

whit f is not continuous in zero

the result is
$$f(+\epsilon)=-\frac{m^24akf(0)}{1-4ak^2}$$

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HallsofIvy
Homework Helper

i need to integrate

$$-(p(y)f(y)')'=m^2w(y)f(y)$$
where
$$p(y)=e^{4ky}(1-4ak^2)$$ and $$w=-4ae^{2y}k\delta(y)$$

but y between [0,infinity[

¿i calculate between $$\int^{epsilon}_0????$$ or ¿i calculate between [-epsilon,epsilon]?????
I have no idea what you are talking about. What are yu integrating? If you are talking about the integral above, if it is given as a definite integral, you use whatever limits of integration are given. If it is given as an indefinite integral (anti-derivative) you do not use any limits of integration.

but, what is??

$$\int^{\epsilon}_0(p(y)f(y)')'dy$$
By the Fundamental Theorem of Calculus, the integral of the derivative of any function is that function:
$$\int^{\epsilon}_0(p(y)f(y)')'dy= p(y)f(y)'$$

whit f is not continuous in zero
If f is not continuous at zero, then it is not differentiable at zero and the integrand above does not exist at 0.

the result is
f(+\epsilon)=-\frac{m^24akf(0)}{1-4ak^2}
Since you haven't actually stated what the problem is, I have no idea whether that is correct or not.

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