Using integration,find the area of the region bounded by the line y= 3x+2, the x-axis and the ordinates x= -2\; and\; x= 1.

 

 

 

 
 
 
 
 

Answers (1)


Required area = \int_{-2}^{\frac{-2}{3}}\left ( 3x+2 \right )dx+\int_{\frac{-2}{3}}^{1}\left ( 3x+2 \right )dx
             = \left | \left [ \frac{\left ( 3x+2 \right )^{2}}{2\times 3} \right ]^{\frac{-2}{3}} _{-2}\right |+\left [ \frac{\left ( 3x+2 \right )^{2}}{6} \right ]^{1}_{\frac{-2}{3}}
         \Rightarrow \left | \left [ \frac{0}{6} \right ]-\left [ \frac{16}{6} \right ] \right |+\left [ \frac{25}{6} \right ]-\left [ \frac{0}{6} \right ]
        \Rightarrow \frac{16}{6}+\frac{25}{6}
       \Rightarrow \frac{41}{6}\: sq.units 

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