Integration of sin(x)

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

Proof:

To prove this, we can use the definition of a derivative. The derivative of -cos(x) is sin(x), which can be shown using the limit definition of a derivative or by recalling the derivative of cosine.

Thus, ∫sin(x) dx = -cos(x) + C.

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