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

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Multiple Choice

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

Explanation:
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.

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