Question

For a constant \[k,\] which expression is the Constant Multiple Rule?

Options

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

• \[\int kf(x)\,dx=\int f(x)\,dx+k\]

• \[\int kf(x)\,dx=k\int f(x)\,dx\]

• \[\int kf(x)\,dx=\frac{1}{k}\int f(x)\,dx\]

Answer 1

A constant factor multiplying the integrand may be taken outside the integral. Thus, \[\int kf(x)\,dx=k\int f(x)\,dx.\]