A Step-by-Step Guide to Finding the Integral of cos(x) with Respect to x

integral of cosx

The integral of cos(x) with respect to x is given by:

∫cos(x) dx = sin(x) + C

where C is the constant of integration

The integral of cos(x) with respect to x is given by:

∫cos(x) dx = sin(x) + C

where C is the constant of integration.

To understand how we arrive at this result, let’s go through the process step by step:

1. Start with the trigonometric identity: sin'(x) = cos(x). This means that the derivative of sin(x) with respect to x is equal to cos(x).

2. By using the fundamental theorem of calculus, which relates the indefinite integral and derivative, we can reverse this process. The integral of cos(x) with respect to x gives us sin(x), up to an arbitrary constant C.

3. Adding the constant of integration, denoted by C, is necessary because integrating simply gives us a family of solutions. Depending on the context, there may be specific conditions that can help determine the value of C.

Therefore, the integral of cos(x) with respect to x is sin(x) + C, where C is any constant.

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