The expression -cos(x) + C is the indefinite integral of which function?

The expression -cos(x) + C is the indefinite integral of which function?

• A. sin x
• B. cos x
• C. tan x
• D. sec x

Answer: (A)

The important idea here is finding the antiderivative, or indefinite integral, of a function. If you differentiate -cos(x), you get sin(x) because the derivative of cos(x) is -sin(x), so d/dx(-cos(x)) = sin(x). That means the antiderivative of sin(x) is -cos(x) + C. Therefore, -cos(x) + C corresponds to integrating sin(x). The other functions have different antiderivatives (cos integrates to sin x + C, tan to -ln|cos x| + C, sec to ln|sec x + tan x| + C), which do not yield -cos(x) + C.

The important idea here is finding the antiderivative, or indefinite integral, of a function. If you differentiate -cos(x), you get sin(x) because the derivative of cos(x) is -sin(x), so d/dx(-cos(x)) = sin(x). That means the antiderivative of sin(x) is -cos(x) + C. Therefore, -cos(x) + C corresponds to integrating sin(x). The other functions have different antiderivatives (cos integrates to sin x + C, tan to -ln|cos x| + C, sec to ln|sec x + tan x| + C), which do not yield -cos(x) + C.