calculus · worked example

Solve ∫ sin(x) dx

Method: standard integral. Verified step-by-step solution with our free AI math solver.
Problem

∫sin⁡(x) dx\int \sin(x) \, dx

Step-by-step solution

  1. Recall: ddx(−cos⁡x)=−(−sin⁡x)=sin⁡x\frac{d}{dx}(-\cos x) = -(-\sin x) = \sin x.

  2. So −cos⁡x-\cos x is an antiderivative of sin⁡x\sin x.

  3. Therefore ∫sin⁡x dx=−cos⁡x+C\int \sin x \, dx = -\cos x + C.

  4. Be careful with signs — the integral of sin⁡\sin is negative cosine; the integral of cos⁡\cos is positive sine.

Answer

−cos⁡(x)+C-\cos(x) + C

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