Question

Which formula is the Sum Rule?

Options

• \[\int kf(x)\,dx=\int k\,dx\int f(x)\,dx\]

• \[\int(f(x)-g(x))\,dx=\int f(x)\,dx+\int g(x)\,dx\]

• \[\int(f(x)+g(x))\,dx=\int f(x)\,dx-\int g(x)\,dx\]

• \[\int(f(x)+g(x))\,dx=\int f(x)\,dx+\int g(x)\,dx\]

Answer 1

Integration is distributive over addition. Therefore, the integral of \[f(x)+g(x)\] equals the sum of the separate indefinite integrals.