/sci/ - Science & Math

[OP !!yzPI6QwWJCg No.4823759]

Sup.
Does anyone have tips regarding how to "reverse" a definite integral?
Or, in a more understandable way: How do you find the integral that gives you a desired value?
The background of my question is just a practice problem from Uni, but the question itself interests me. In the case of the Uni problem, it was rather simple; The function must not be constant, and the value of the integral must equal 7. Any hints?

[Anonymous No.4823766]

it's impossible for any integral of a non-constant function to be a constant

because the derivative of a constant is a constant (namely, 0)

either that or I'm just not getting the question

[Anonymous No.4823774]

using polynomials, you can make a definite integral with any value. in fact, you can do it with any given polynomial degree and integral interval using scalars:
for example, the integral of x^2 from 0 to 1 is 1/3, so the integral of 21*x^2 from 0 to 1 is 7, which should be a solution to your problem.

you could also take 7/4*x^3 from 0 to 2. as a general rule in calculus, you can pretty much design a polynomial to do whatever you need.

[Anonymous No.4823782]

>>4823774
here

i also just realized that you can simply use a linear function to do what you need. suppose you want the area to be 7, just integrate 7x/2 from 0 to 2. you basically just have to use geometry to make a triangle of the desired area, and then make it into a function. it's the same idea as using polynomials except this is much easier since it's linear.