indefinite integrals

Question

The integral ∫sin(x) dx equals

RankGuru · Accepted Answer

1. **Standard Integral**: The integral of a trigonometric function is the reverse process of differentiation.
2. **Reasoning**: Since $\frac{d}{dx}(\cos x) = -\sin x$, it follows that $\frac{d}{dx}(-\cos x) = \sin x$.
3. **Result**: Therefore, $\int \sin x \, dx = -\cos x + C$.
4. **Caution**: Students often confuse this with the derivative of $\sin x$ (which is $+\cos x$). Reminder: Integration of $\sin$ is negative $\cos$.

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indefinite integrals

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More indefinite integrals Practice Questions

Evaluate $\int e^x (\frac{1+x\ln x}{x}) dx$ (Assume $x > 0$ and base $e$ for $\ln$ ).

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indefinite integrals

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More indefinite integrals Practice Questions

Evaluate ∫ex(1+xln⁡xx)dx\int e^x (\frac{1+x\ln x}{x}) dx∫ex(x1+xlnx​)dx (Assume x>0x > 0x>0 and base eee for ln⁡\lnln).

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