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what is the integral of sinx\sin x

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Q. what is the integral of sinx\sin x
  1. Identify Function: Identify the function to integrate.\newlineWe are asked to find the integral of the function sin(x)\sin(x).
  2. Recall Integral: Recall the integral of sin(x)\sin(x). The integral of sin(x)\sin(x) with respect to xx is a standard integral in calculus. We know that the derivative of cos(x)-\cos(x) is sin(x)\sin(x), so the integral of sin(x)\sin(x) should be cos(x)-\cos(x).
  3. Write Antiderivative: Write down the antiderivative.\newlineThe antiderivative of sin(x)\sin(x) is cos(x)-\cos(x) plus the constant of integration, CC.\newlinesin(x)dx=cos(x)+C\int \sin(x) \, dx = -\cos(x) + C
  4. Check for Errors: Check for any mathematical errors.\newlineWe can differentiate our result to check if we get back the original function. The derivative of cos(x)-\cos(x) is sin(x)\sin(x), which is our original function.

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