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Question

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

A
True
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B
False
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Solution

The correct option is B True
Let ddxF(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

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