Constructing funcions from integrals

[Gchem45]

Ok I have a great deal of problems of these variety to do and have no clue about how to approach them. I'm a chemistry major so I don't get to devote too much time to calc. but I catch on pretty quick. So, if someone could explain how to do one I'm sure the rest will fall into place. So, the first question is:
-Construct a function f(x) such that integral of f(x) from x=1 to infinity equals 232.

Like I stated before this is one of many problems in many different varieties, however I think that if I know how to solve one I can hopefully do the rest. Thanks in advance

 

[royhaas]

There are many such functions, for example, \(\displaystyle f(x)=232/x^2\).

 

[pka]

I sincerely hope that a mathematics professor did not construct this problem! The reason being that there is not unique answer. I will give two possible correct answers. Realize that there are many more.
\(\displaystyle \L f(x) = \frac{{232}}{{x^2 }}\quad \& \quad g(x) = \frac{{232}}{{e^{x - 1} }}\)

 

[Gchem45]

Awesome thanks guys that helped me answer a bunch of them but there is this one that is giving me trouble still.
-Create f(x) so that the integral from 1 to 232 = infinity.

I was thinking some sort of tangent fuction with its vertical asymptote rigtht around 232 but I havent had much success with that strategy. I'm probably just being retarded but I'm just so fried from finals I just am drawing a blank. Thanks again.

 

[pka]

\(\displaystyle \L f\left( x \right) = \frac{{ - 1}}{{x - 232}}\quad \& \quad \int\limits_a^b {f(x)dx} = - \ln \left| {b - 232} \right| + \ln \left| {a - 232} \right|.\)