Integrate a function multiple times;

1) I'm given: f(x) = x^2 - 3x - 5

I'm asked: "in which of the infinite integrals of f(x) does it take the value of 5 with x = 3?"

I thought of doing maybe a cycle with conditions inside until it finds the answer but I couldn't find a way to do it. Is there maybe a function that allows me to obtain for example the tenth integral of f(x) ? Something like int('x^2 - 3*x - 5',H) where H stands for 10 meaning it will return the function integrated 10 times.

2)Given g(x) = x^2 + 3x , find the integral in which its graphical representation passes through the point p(1,3)

I'm guessing this one is similar to 1), I'll have to do a cycle with conditions. Although the part that says that passes through p(1,3) don't really know how to verify it.

I'd appreciate very much any help.

[Matt J]

What about the integration constants? Are we assuming zero initial conditions?

I thought of doing maybe a cycle with conditions inside until it finds the answer

I'm not sure that would satisfy the assignment. You are asked for all of the integrals that would satisfy this, not just the first one.

[Ramses Estay]

Doesn't say anything so I also assume the zero initial conditions. In the question it says what's the integral that satisfies the condition. Even if there are multiple answers, just finding the first one should be enough.

[Roger Stafford]

In view of the wording of your problem, "in which of the infinite integrals of f(x) does it take the value of 5 with x = 3?", I suspect you have misinterpreted the problem, Ramses. By "infinite integrals" I doubt that they mean integrating your function multiple times. I suspect they are referring to the arbitrary constant of integration after just one integration. There are infinitely many such possible constants but only one would satisfy the stated condition. In other words in problem 1) you are being asked, in effect, what is the constant of integration for the indefinite integral of f(x) such that it has a value of 5 at x = 3. If so, this is a trivial problem in calculus which you can just about solve in your head without using matlab. The same can be said of the second problem.

[Matt J]

That makes a lot more sense, now that I look at it again! Badly worded problem, though.

[Ramses Estay]

Yes Roger, you are completely right. I misinterpreted the problem, I asked a teacher too and it's as you said, for which it's a pretty easy problem. Thanks Matt for taking your time to read it too; I was able to do them now. I apologize for my english, as it isn't my native language.