How to Integrate sin x?

To integrate the function sin x, we need to find the antiderivative. The integral of sin x with respect to x is a well-known result in calculus.

The integral is given by:

 ∫ sin x dx = -cos x + C

where C is the constant of integration. This means that when you take the integral of sin x, you get -cos x plus a constant.

Let’s break this down:

• Function Understanding: The function sin x represents the sine of an angle x in radians.
• Derivative Knowledge: Knowing the derivative of the cosine function helps here. The derivative of -cos x is sin x.
• Constant of Integration: When performing indefinite integration, we always add C to account for all possible antiderivatives.

In summary, the integral of sin x can be easily computed and results in -cos x + C. This is a fundamental aspect of calculus and is widely used in various applications.