Question 6 (1 point)
\[
\int \sin (2 \pi) d x=
\]
a) $-\cos (2 \pi)+C$
b) $\sin (2 \pi) x+C$
c) $-\cos (2 \pi) x+C$
d) $x+C$

Answer

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Answer

None of the given options are correct. The correct answer should be $\boxed{C}$.

Steps

Step 1 ：The integral of a constant (which is what sin(2π) is, as sin(2π) = 0) with respect to x is just the constant times x.

Step 2 ：Therefore, the integral of sin(2π) dx is 0*x + C, which simplifies to just C.

Step 3 ：However, this option is not available in the choices given.

Step 4 ：The closest option to the correct answer is d) x + C, but this is not exactly correct.

Step 5 ：None of the given options are correct. The correct answer should be $\boxed{C}$.