Question

What does \[A(x)=\int_a^x f(t)\,dt\] give?

Options

• The constant of integration from \(a\) to \(b\)

• The derivative of \(f(t)\) from \(a\) to \(x\)

• The area accumulated from \(x=x\) to \(x=b\)

• The area accumulated from \(x=a\) to a variable point \(x\)

Answer 1

The value \(A(x)\) represents the area accumulated beginning at \(x=a\).
As the variable point \(x\) changes, the accumulated area changes accordingly.