∫ cf(x)dx
To integrate the function cf(x)dx, where c is a constant and f(x) is any function, we can use the property of integration known as the constant multiple rule
To integrate the function cf(x)dx, where c is a constant and f(x) is any function, we can use the property of integration known as the constant multiple rule.
The constant multiple rule states that if we have a constant c multiplied by a function, we can simply bring the constant outside the integral and integrate the function as usual. Mathematically, the constant multiple rule can be stated as follows:
∫ cf(x)dx = c ∫ f(x)dx
Using this property, we can solve the given integral as follows:
∫ cf(x)dx = c ∫ f(x)dx
Therefore, the result of integrating cf(x)dx is equal to the constant c multiplied by the integral of f(x)dx.
It is worth noting that this rule holds true for any constant c, whether it is positive, negative, or zero.
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