Answer: The antiderivative of the cosine function is the sine function, and the antiderivative of the sine function is the negative cosine function, with an arbitrary constant of integration added in each case.
In symbols:
∫ cos(x) dx = sin(x) + C
∫ sin(x) dx = -cos(x) + C
Here, C represents an arbitrary constant of integration, which is added to the antiderivative since the derivative of a constant is zero. These antiderivatives can be used to evaluate definite integrals involving the sine and cosine functions, and they are also important in calculus and physics, where they appear in many applications.
Explanation: