Calculating the Integral of sin x | Techniques and Understanding

integral(sin x)

The integral of sin x can be calculated using integration techniques

The integral of sin x can be calculated using integration techniques.

The integral of sin x is equal to -cos x + C, where C is the constant of integration.

To understand why this is the case, we need to consider the derivative of -cos x.

The derivative of -cos x with respect to x is sin x. This is known as the derivative of the cosine function.

When we calculate the integral of a function, we are essentially finding the function whose derivative is equal to that of the given function.

Since the derivative of -cos x is sin x, the integral of sin x must be -cos x (plus a constant of integration, C).

So, the integral of sin x is -cos x + C.

This result can also be visually understood by graphing the function sin x and recognizing that the integral represents the area under the curve of the function.

It’s important to note that when calculating definite integrals, which involve finding the area between two values of x, the constant of integration is not needed.

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