How to Evaluate the Integral of sin x with Respect to x

∫ sin x dx

The integral of sin x with respect to x can be evaluated as follows:

∫ sin x dx = – cos x + C

where C is the constant of integration

The integral of sin x with respect to x can be evaluated as follows:

∫ sin x dx = – cos x + C

where C is the constant of integration.

To derive this result, we can use the well-known integral formula:

∫ cos x dx = sin x + C

Which is the antiderivative of cos x. By differentiating both sides of this equation, we can find the integral of sin x.

Differentiate both sides with respect to x:

d/dx (∫ cos x dx) = d/dx (sin x + C)

Now, the left side is just cos x (since the derivative of an integral is the original function) and the right side becomes:

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

cos x = cos x

This equation is true for all values of x, hence, the integral of sin x is simply – cos x plus a constant of integration, C.

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