Question

Which formula is the Difference Rule?

Options

• \[\int kf(x)\,dx=k+\int f(x)\,dx\]

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

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

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

Answer 1

The Difference Rule separates subtraction into two integrals. The integral of the first function is retained, and the integral of the second function is subtracted.