∫ 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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