Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the integral of cos(x)?

1. sin(x)

2. -sin(x)

3. cos(x)

4. -cos(x)

The correct answer is: sin(x)

The integral of cos(x) with respect to x is indeed sin(x), which aligns with what you're referring to as the correct answer. When performing integration, the function's behavior and properties come into play. The cosine function is an even function, meaning it is symmetric about the y-axis, and it integrates to the sine function. This relationship arises from the fundamental concepts of differentiation and integration: the derivative of sin(x) is cos(x). Thus, integrating cos(x) leads to the original function that, when differentiated, yields cos(x). In summary, the process of finding the integral of cos(x) hinges on understanding the fundamental relationships between trigonometric functions, particularly how sine and cosine derivatives are linked, ultimately leading to the conclusion that the integral is sin(x).