Question

Using integration find the area of a triangular region whose sides have the equation $y=x+1,y=2x+1$ and $x=2$.
(Draw the figure in answer book)

Answer 1

The equations given are

$y=2x+1$

$y=x+1$

$x=2$

Solving these, we get the coordinates of the vertices of the triangle formed by these.

$(0,1),(2,3),(2,5)$

Area enclosed by these lines forming triangle is:

$A={\int }_0^2(2x+1-(x+1\left)\right)dx$

$A={\int }_0^2\left(x\right)dx$

$A={\left[\frac{x^2}{2}\right]}_0^2=2sq.units$