Deriving the Integral of Sin(x) Using Trigonometric Integration Techniques

∫sin(x)dx

To find the integral of sin(x), we can use the integration techniques for trigonometric functions

To find the integral of sin(x), we can use the integration techniques for trigonometric functions. The integral of sin(x) is given by:

∫sin(x)dx = -cos(x) + C

where C is the constant of integration.

The above result can be obtained using the integration formula for sine function. The integral of sin(x) is equal to -cos(x) plus the constant of integration.

Let’s see how we can derive this result:

We know that the derivative of cos(x) is -sin(x). So, if we differentiate -cos(x) with respect to x, we will get -(-sin(x)) which simplifies to sin(x).

Therefore, ∫-cos(x)dx = -cos(x) + C

So the integral of sin(x) is equal to -cos(x) plus the constant of integration.

Hence, the integral of sin(x) is ∫sin(x)dx = -cos(x) + C, where C is the constant of integration.

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