In calculus, finding the integral of trigonometric functions is a common task. One of the most fundamental integrals is the integral of \(\sin(x)\). In this short article, we will explore how to find the integral of \(\sin(x)\).
Finding the Integral
The integral of \(\sin(x)\) can be found using basic integration rules. We know that the derivative of \(\cos(x)\) is \(-\sin(x)\). Therefore, to reverse this process and find the integral of \(\sin(x)\), we can write:
\[ \int \sin(x) \, dx = -\cos(x) + C \]
Here, \(C\) is the constant of integration, which appears because the process of integration can produce multiple functions differing by a constant.
The integral of \(\sin(x)\) is \( \boxed{-\cos(x) + C} \). Understanding this basic integral is crucial for solving more complex problems in calculus involving trigonometric functions.
