Understanding Integration | The Integral of 1 with Respect to u

∫1du

The integral of 1 with respect to u, denoted as ∫1 du, can be evaluated to obtain a solution

The integral of 1 with respect to u, denoted as ∫1 du, can be evaluated to obtain a solution. When integrating a constant function like 1, the result is simply the variable u. Therefore, ∫1 du = u + C, where C is the constant of integration.

To understand this further, let’s break down the process of integration.

Integration is the reverse operation of differentiation. It aims to find the antiderivative of a given function. In our case, the function is 1, which is a constant.

When integrating a constant, the result is a function that is linear and increases at a constant rate. It is represented by a straight line with a slope of 1. The variable u represents this linear function.

The “du” notation here indicates the variable we are integrating with respect to. This signifies that we are treating u as the independent variable and integrating with respect to it.

By integrating the constant function 1 with respect to u, we find that the antiderivative is u. However, since the result of integration is not unique and can differ by a constant value, we include the constant of integration, denoted as C. This constant accounts for the infinite number of possible functions that have the same derivative (in this case, the constant function 1).

Therefore, the solution to ∫1 du is u + C.

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