Question

If \(f\) is continuous on an interval, which expression defines the area function?

Options

• \[A(x)=\int_x^a f(t)\,dt\]

• \[A(x)=\int_a^x f(t)\,dt\]

• \[A(x)=\int_a^b f(x)\,dx\]

• \[A'(x)=\int_a^x f(t)\,dt\]

Answer 1

For a continuous function \(f\), the area function is \(A(x)=\int_a^x f(t)\,dt\).
Its lower limit is the fixed point \(a\), while its upper limit is the variable point \(x\).