antiderivative of sinx
The antiderivative (also known as the integral) of sin(x) is -cos(x) + C, where C is the constant of integration
The antiderivative (also known as the integral) of sin(x) is -cos(x) + C, where C is the constant of integration.
To understand how we arrive at this result, let’s start with the derivative of the function -cos(x). The derivative of -cos(x) with respect to x is sin(x), using the chain rule of differentiation. This means that -cos(x) is an antiderivative of sin(x), as its derivative matches the original function.
However, it is important to note that the antiderivative is not unique. Due to the periodic nature of sine and cosine functions, we have an infinite number of antiderivatives for sin(x). These are given by -cos(x) + 2πn, where n is an integer representing the number of complete cycles.
For example, if we write the general antiderivative for sin(x) as -cos(x) + C, where C is the constant of integration, we can rewrite it as -cos(x) + 2πn, where n is an integer. Both expressions are correct and represent the same family of functions.
More Answers:
The Chain Rule: Finding the Derivative of e^u with Respect to xDerivative of a^u: Understanding the Chain Rule for Exponential Functions
Understanding Logarithmic Differentiation: How to Find the Derivative of log_a(u)