Question

Fill in the blanks: The signed area between the graph of a continuous function f and the x-axis on [a, b] is represented by the notation _______ and is called the _______.

Short answer

The signed area between the graph of a continuous function f and the x-axis on [a, b] is represented by the notation ${\int }_a^{b}f\left(x\right)dx$ and is called the integral of f on [a, b].

Step-by-step solution

Step 1. Given information

The signed area between the graph of a continuous function f and the x-axis on [a, b] is represented by the notation _______ and is called the _______.

Step 2. Answer

The area under the curve f or between f and x-axisis given by integration of f within specified limits on x- axis.

it is obtained from assuming collective or integrated area of small rectangles of width dx

The signed area between the graph of a continuous function f and the x-axis on [a, b] is represented by the notation ${\int }_a^{b}f\left(x\right)dx$and is called the integral of f on [a, b].