Calculate the integral ∫ (sin(2x)) dx. What is the result?

To find the integral of sin(2x) with respect to x, we can apply a standard technique involving substitution or using the integration formula for sine functions.

When integrating sin(kx), the general rule is:

∫ sin(kx) dx = - (1/k) cos(kx) + C

In this context, k equals 2 for the function sin(2x). Therefore, we substitute k with 2:

∫ sin(2x) dx = - (1/2) cos(2x) + C

This result indicates that for every increment of x, the area under the curve defined by sin(2x) is reflected as a negative cosine function scaled by 1/2, plus an arbitrary constant C.

Thus, the correct result of the integral is indeed -(1/2) cos(2x) + C, which confirms the first choice provided in the question.

Other options, which suggest different outcomes, do not adhere to the correct application of integration rules for sine functions.