The indefinite integral of sin(x) with respect to x equals which expression?

The indefinite integral of sin(x) with respect to x equals which expression?

• A. -cos(x) + C
• B. cos(x) + C
• C. sin(x) + C
• D. -sin(x) + C

Answer: (A)

Finding an antiderivative means finding a function whose derivative is the given function. For sin x, a function whose derivative is sin x is -cos x, because the derivative of cos x is -sin x. Differentiating -cos x gives sin x, so the indefinite integral is -cos x + C. The constant C accounts for any vertical shift and is necessary for the most general antiderivative.

Finding an antiderivative means finding a function whose derivative is the given function. For sin x, a function whose derivative is sin x is -cos x, because the derivative of cos x is -sin x. Differentiating -cos x gives sin x, so the indefinite integral is -cos x + C. The constant C accounts for any vertical shift and is necessary for the most general antiderivative.