Question

If some portion of the curve is above $X$-axis and some is below the $X$-axis as shown below.

Area bounded by the curve, $X$-axis and ordinates is given by

• A. $A=A_1+A_2$
• B. $A=A_1+\left|A_2\right|$
• C. $A=\left|A_1\right|+A_2$
• D. None of these

Answer 1

Answer: (C)

Generally, it may happen that some portion of the curve is above $X$-axis and some is below the $X$-axis as shown in the figure. Here, $A_1<0$ and $A_2>0$. Therefore, the area $A$ bounded by the curve $y=f(x), X$-axis and the ordinates $x=a$ and $x=b$ is given by
$A=\left|A_1\right|+A_2$