Understanding the Antiderivative of cos(x): Application and Constant of Integration

antiderivative of cosx

The antiderivative of cos(x) is sin(x) + C, where C is the constant of integration

The antiderivative of cos(x) is sin(x) + C, where C is the constant of integration.

To understand why the antiderivative of cos(x) is sin(x), we can differentiate sin(x) to confirm that its derivative is indeed cos(x):

d/dx(sin(x)) = cos(x)

Now, using the reverse process, we want to find the function that, when differentiated, gives us cos(x). This is known as finding the antiderivative (or primitive) of cos(x).

We know that the derivative of sin(x) is cos(x), so we can say that the antiderivative of cos(x) is sin(x) plus some constant C. Adding a constant is necessary because when we differentiate a constant, it becomes zero, so adding it does not affect the derivative.

Therefore, the antiderivative of cos(x) is sin(x) + C, where C is the constant of integration.

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