Find the area of the region bounded by the line `y=3x+2`, the x-axis and the ordinates `x=-1` and `x=1`

Explanation

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


So, The Required area `=int_{-1}^{frac{-2}{3}}(3 x+2) d x+int_{-frac{2}{3}}^{1}(3 x+2) d x`

`=[frac{3 x^{2}}{2}+2 x]_{-1}^{-frac{2}{3}}+[frac{3 x^{2}}{2}+2 x]_{-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