Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What does the integral of sin(x) yield?

1. -cos(x)

2. cos(x)

3. sin(x)

4. -sin(x)

The correct answer is: -cos(x)

The integral of sin(x) yields -cos(x) because the process of integration is about finding the antiderivative of a function. When you integrate sin(x), you are looking for a function whose derivative is sin(x). The derivative of -cos(x) is indeed sin(x), which confirms that -cos(x) is the correct antiderivative. This relationship stems from the basic properties of trigonometric functions and their derivatives: the sine function is the derivative of the negative cosine function. Understanding this relationship is essential in calculus and highlights how integrals and derivatives are interconnected through inverse operations.