Applying the Constant Rule of Integration: Integral of cf(x)dx

∫ cf(x)dx

To find the integral of the function cf(x)dx, where c is a constant and f(x) is a function, you can apply the constant rule of integration

To find the integral of the function cf(x)dx, where c is a constant and f(x) is a function, you can apply the constant rule of integration.

The constant rule states that if you have a constant multiplied by a function, you can bring the constant outside the integral and integrate the function as usual.

So, for ∫ cf(x)dx, we can rewrite it as c∫ f(x)dx.

Now, you can integrate f(x) as you normally would, treating c as a constant. The integral of f(x) is denoted as F(x), so the result would be cF(x) + C, where C is the constant of integration.

To summarize:

∫ cf(x)dx = c∫ f(x)dx = cF(x) + C

Note that the constant c remains outside the integral and is not affected by the integration process. Also, don’t forget to add the constant of integration, C, to your final answer.

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