Integration of an integrable function fx gives a family
| Integration of an integrable function f(x) gives a family of curves which differ by a constant value.
A. True
B. False
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Let ddx(F(x)) = f(x).
We saw that in that case, ∫f(x)=F(x)+C, where c is any number.
We know that the functions F(x) and F(x)+5 are different. So, as we change c, we get different functions. This means, when we integrate a function, we get a collection of functions, which differ by a constant. For example, if we integrate 2x, we will get functions of the form x2+k, where k is a constant. If we plot those graphs for different values of k, we will get the following figure
