Question

Draw the graph of 2x+y=6 and 2x-y+2=0 shaded the region bounded by thes lines and x axis find the area of the shaded region

Answer 1

Answer:

2x+y =6 .............(i)  

Find points on x-axis and y-axis by putting y=0 and x=0  

The points are A(3,0) and B(0,6) .Join AB  

2x -y +2 = 0 ........................(ii)  

here points will be P(-1,0) and Q(0,2) Join PQ  

Find the point of intersection of (i) and (ii) by adding  

4x =4 or x =1 and y =4.................(iii)  

Area of the region below (i) line taking limits from 1 to 3  

integrate[6-2x]  

6x -x^2 and take limits from 1 to 3  

[18 - 9]- [6-1] = 9 -5 =4 square units...................Ans  

Area below (ii) line  

integral [2x+2] taking limits from -1 to+1  

[x^2 +2x] take limits from -1 to+1  

[1+2] - [1-2] = 3 +1 = 4 square units.........................Ans  

Total area = 4+4 = 8 square units

Answer 2

2x+y =6 .............(i)  

Find points on x-axis and y-axis by putting y=0 and x=0  

The points are A(3,0) and B(0,6) .Join AB  

2x -y +2 = 0 ........................(ii)  

here points will be P(-1,0) and Q(0,2) Join PQ  

Find the point of intersection of (i) and (ii) by adding  

4x =4 or x =1 and y =4.................(iii)  

Area of the region below (i) line taking limits from 1 to 3  

integrate[6-2x]  

6x -x^2 and take limits from 1 to 3  

[18 - 9]- [6-1] = 9 -5 =4 square units...................Ans  

Area below (ii) line  

integral [2x+2] taking limits from -1 to+1  

[x^2 +2x] take limits from -1 to+1  

[1+2] - [1-2] = 3 +1 = 4 square units.........................Ans  

Total area = 4+4 = 8 square units