Question

Which expression gives physical area when the curve \[y=f(x)\] lies below the \[x\]-axis from \[x=a\] to \[x=b\]?

Options

• \[\text{Area}=\left|\int_a^b f(x)\,dx\right|\]

• \[\text{Area}=\int_a^b f(x)\,dx\]

• \[\text{Area}=A_1+A_2\]

• \[\text{Area}=\int_c^d g(y)\,dy\]

Answer 1

Physical area cannot be negative, even though the definite integral below the \[x\]-axis is negative. The absolute value (modulus) of the integral must be taken.