Question

A curve crosses the \[x\]-axis, forming area \[A_1\] below the axis and area \[A_2\] above the axis. What is its total area?

Options

• \[\text{Total Area }A=\int_a^b y\,dy\]

• \[\text{Total Area }A=A_1+A_2\]

• \[\text{Total Area }A=|A_1|+A_2\]

• \[\text{Total Area }A=|A_1|-A_2\]

Answer 1

The area \[A_1\] below the \[x\]-axis must be counted by its absolute value. It is then added to the positive area \[A_2\] above the axis.