Thank you for reporting, we will resolve it shortly
Q.
The area of the region bounded by the line $y=3 x+2$, the $X$-axis and the ordinates $x=-1$ and $x=1$ is
Application of Integrals
Solution:
As shown in the figure, the line $y=3 x+2$ meets $x$-axis at $x=\frac{-2}{3}$ and its graph lies below $X$-axis for $x \in\left(-1, \frac{-2}{3}\right)$ and above $X$-axis for $x \in\left(\frac{-2}{3}, 1\right)$.
The required area $=$ Area of the region $A C B A$
+ Area of the region ADEA
$ =\left|\int\limits_{-1}^{\frac{-2}{3}}(3 x+2) d x\right|+\int\limits_{\frac{-2}{3}}^1(3 x+2) d x $
$ =\left|\left[\frac{3 x^2}{2}+2 x\right]_{-1}^{\frac{-2}{3}}\right|+\left[\frac{3 x^2}{2}+2 x\right]_{\frac{-2}{3}}^1$
$=\frac{1}{6}+\frac{25}{6}=\frac{13}{3}$ sq units
