Question

Which formula states the General Linearity Rule, where \[k_1,k_2,\ldots,k_n\] are real constants?

Options

• \[\int[k_1f_1(x)+k_2f_2(x)]\,dx=k_1k_2\int[f_1(x)+f_2(x)]\,dx\]

• \[\int[k_1f_1(x)+k_2f_2(x)]\,dx=\int f_1(x)\,dx+\int f_2(x)\,dx+k_1+k_2\]

• \[\int[k_1f_1(x)+k_2f_2(x)+\cdots+k_nf_n(x)]\,dx=k_1\int f_1(x)\,dx+k_2\int f_2(x)\,dx+\cdots+k_n\int f_n(x)\,dx\]

• \[\int[k_1f_1(x)-k_2f_2(x)]\,dx=k_1\int f_1(x)\,dx+k_2\int f_2(x)\,dx\]

Answer 1

General linearity combines the sum rule and the constant multiple rule. Each real constant remains with its corresponding separate indefinite integral.