reverse integrals


by Big-Daddy
Tags: integrals, reverse
Big-Daddy
Big-Daddy is offline
#1
Jan14-14, 02:54 PM
P: 340
I need to find a function f(x) such that

[tex]\int_{-\infty}^{100+10n} (f(x)) dx = 1-0.1^n[/tex]

for n=1,2,3,4,5,6...∞. How would I go about this? It must be exponential in some way I'm guessing?

This is not a homework problem. I don't just want the answer. I want guidance on this type of problem and function, but please from someone with an idea of how to answer this particular case too ...
Phys.Org News Partner Mathematics news on Phys.org
Math modeling handbook now available
Hyperbolic homogeneous polynomials, oh my!
Researchers help Boston Marathon organizers plan for 2014 race
mathman
mathman is offline
#2
Jan14-14, 03:12 PM
Sci Advisor
P: 5,941
Replace (100+10n) by a real variable (y). Take the derivative of both sides, this will give you an expression for f(y) if it exists. It will be an exponential.
Big-Daddy
Big-Daddy is offline
#3
Jan14-14, 05:18 PM
P: 340
Quote Quote by mathman View Post
Replace (100+10n) by a real variable (y). Take the derivative of both sides, this will give you an expression for f(y) if it exists. It will be an exponential.
So y=100+10n, n = 1/10(y-100) = (1/10)y-10.

Now what? I need to bear the integral limits (-∞ to y) in mind...

mathman
mathman is offline
#4
Jan15-14, 03:20 PM
Sci Advisor
P: 5,941

reverse integrals


0.1n = 0.1(y-100)/10 = exp((y-100)ln(0.1)/10). Now take the derivatives of both sides to get f(y) = .


Register to reply

Related Discussions
Using double integrals to evaluate single integrals Calculus 9
Changing cartesian integrals to equivalent polar integrals. Calculus & Beyond Homework 5
Triple Integrals. Need help ASAP! I cant figure out why 2 integrals arent matching up Calculus & Beyond Homework 1
Question about Gaussian Integrals and Path Integrals General Physics 2
Finite-part integrals (Hadamard) integrals with Mathematica Math & Science Software 11