Compute ∫ cos x dx.

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Multiple Choice

Compute ∫ cos x dx.

Explanation:
When you integrate cos x, you’re finding a function whose derivative is cos x. Since the derivative of sin x is cos x, the antiderivative is sin x plus a constant. So ∫ cos x dx = sin x + C, and you can check by differentiating: d/dx [sin x + C] = cos x. The other forms don’t work because differentiating them gives different results (for example, cos x differentiates to -sin x, -cos x differentiates to sin x, and -sin x differentiates to -cos x).

When you integrate cos x, you’re finding a function whose derivative is cos x. Since the derivative of sin x is cos x, the antiderivative is sin x plus a constant. So ∫ cos x dx = sin x + C, and you can check by differentiating: d/dx [sin x + C] = cos x. The other forms don’t work because differentiating them gives different results (for example, cos x differentiates to -sin x, -cos x differentiates to sin x, and -sin x differentiates to -cos x).

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