Class 12

Math

Calculus

Application of Integrals

Using integration find the area of the triangular region whose sides have the equations $y=2x+1,y=3x+1$ and $x=4$

On solving these question, we obtain the vertices of triangle as $A(0,1),B(4,13)$, and $C(4,9)$.

It can be observed that,

$Area(ΔACB)=Area(OLBAO)−Area(OLCAO)$

$=∫_{0}(3x+1)dx−∫_{0}(2x+1)dx$

$=[23x_{2} +x]_{0}−[22x_{2} +x]_{0}$

$=(24+4)−(16+4)$

$=28−20=8$sq. units.