Question

The area bounded by the line y=x , x axis and ordinates x = -1 and x=2
A.3/2
B.5/2
C.2
D.3

Answer 1

Hint: x=a is the form of line which is parallel to y axis and situated at the distance of ‘a’ unit from origin and y=a is the form of line which is parallel to x axis and situated at the distance of ‘a’ unit from origin. If ‘a’ is positive then it will be on the right side of the origin and if ‘a’ is negative then it will be on the left side of the origin. By using this information, draw given lines. Finally we will have two right angled triangles. Now apply the formulae of the area of the triangle to get the required result.

Complete step-by-step answer:
Draw the x= -1 which is parallel to y axis and and situated on the left side of origin at distance of 1 unit, x=2 which is parallel to y axis situated on the right side of origin at distance of 2 unit and y=x which is line going through origin and maintaining equal distance from both axis.

Here, we have two right angled triangles COD and AOB. By the formula of area of a right angled triangle we will find required area.
In triangle COD, CO is base and CD is height.
CO =1 and CD =1
Area of COD
   $ \begin{align}
  & =\dfrac{1}{2}\times base\times height \\
 & =\dfrac{1}{2}\times CO\times CD \\
 & =\dfrac{1}{2}\times 1\times 1 \\
 & =\dfrac{1}{2} \\
\end{align} $
 In triangle AOB, OB is base and AB is height.
OB= 2 and AB = 2
Area of AOB is
 $ \begin{align}
  & \dfrac{1}{2}\times base\times height \\
 & =\dfrac{1}{2}\times OB\times AB \\
 & =\dfrac{1}{2}\times 2\times 2 \\
 & =2 \\
\end{align} $
Required area is = Area of triangle COD + Area of triangle AOB
  $ \begin{align}
  & =\dfrac{1}{2}+2 \\
 & =\dfrac{5}{2} \\
\end{align} $
Option (B) is correct.

Note:Here we can also find out the area by using integral. The above method is not a general method, it is only used when the required region forms a triangle, otherwise we will use integral to find the area.