Understanding the Antiderivative of Sin x: An In-depth Analysis and Integration Techniques

Antiderivative of sin x

The antiderivative of sin x can be found by integrating the function

The antiderivative of sin x can be found by integrating the function.

The integration of sin x can be done using a few different methods. One method is to use the trigonometric identity:

∫sin x dx = -cos x + C

where C is the constant of integration.

To understand how this result is derived, we can start by considering the derivative of cos x.

If we differentiate cos x with respect to x, we get:

d/dx (cos x) = -sin x

Therefore, if we integrate -sin x with respect to x, we can recover the original function, sin x.

∫ -sin x dx = cos x + C

However, since we are looking for the antiderivative of sin x, we must add a negative sign in front:

-∫sin x dx = -cos x + C

Simplifying, we get:

∫sin x dx = cos x + C

So, the antiderivative of sin x is cos x plus a constant.

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