Question

Find the area bounded by line $y=3x+2$, x-axis and ordinates $x=-1$ and $x=1$.

Answer 1

$y=3x+2,x=-1,x=1$

$Requiredarea$$=\left|{\int }_{-1}^{\frac{-2}{3}}(3x+2)dx\right|+{\int }_{-\frac{2}{3}}^1(3x+2)dx=\left|{[\frac{{3x}^2}{2}+2x]}_{-1}^{-\frac{2}{3}}\right|+{[\frac{{3x}^2}{2}+2x]}_{-\frac{2}{3}}^1=|\frac{2}{3}-\frac{4}{8}-(\frac{3}{2}-2)|+\frac{3}{2}+2-(\frac{2}{3}-\frac{4}{3})=|-\frac{2}{3}+\frac{1}{2}|+\frac{7}{2}+\frac{2}{3}=|-\frac{1}{6}|+\frac{25}{6}=\frac{1}{6}+\frac{25}{6}=\frac{13}{3}squnit$