Mastering the Integral of Sin(x) with Respect to x Using the Integration Rules and Derivative Proof

sin(x)dx

To find the integral of sin(x) with respect to x, we can use the integration rules

To find the integral of sin(x) with respect to x, we can use the integration rules.

The integral of sin(x) can be evaluated by applying the integral formula for the sine function, which is:

∫ sin(x)dx = -cos(x) + C

where C is the constant of integration.

We can prove this by taking the derivative of -cos(x) + C with respect to x:

d/dx(-cos(x) + C) = (d/dx)-cos(x) + (d/dx)C
= sin(x) + 0 = sin(x)

Therefore, the integral of sin(x) is indeed -cos(x) + C, where C is the constant of integration.

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