Mastering Integration | The Integral of Cos(x) and Constant of Integration Explained

∫ cos x dx

To find the integral of cos(x) with respect to x, we can use the basic rules of integration

To find the integral of cos(x) with respect to x, we can use the basic rules of integration. In this case, the integral of cos(x) is given by:

∫ cos(x) dx = sin(x) + C

Here, C represents the constant of integration, which accounts for the fact that the derivative of a constant is 0. Therefore, when we integrate a function, we add a constant term to the result.

So, the definite integral of cos(x) with respect to x would be:

∫ cos(x) dx = sin(x) + C

It is important to note that the indefinite integral of cos(x) can also be written as:

∫ cos(x) dx = sin(x) + C1

where C1 is another constant of integration. This represents the infinite family of antiderivatives of cos(x), all of which differ by a constant value.

In summary, the integral of cos(x) with respect to x is sin(x) plus a constant, given by ∫ cos(x) dx = sin(x) + C.

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