Question

Integration of an integrable function f(x) gives a family of curves which differ by a constant value.

• A. True
• B. False

Answer 1

The correct option is A

True

Let $\frac{d}{dx}F\left(x\right)=f\left(x\right).$

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 $x^2+k$, where k is a constant. If we plot those graphs for different values of k, we will get the following figure