Draw the graph of 2x + y = 6 and 2x – y + 2 = 0, shade the regionbou

1.	Draw the graph of 2x + y = 6 and 2x – y + 2 = 0, shade the regionbounded by these lines and x - axis. Find the area of the shaded.region.
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

Draw the graph of 2x + y = 6 and 2x – y + 2 = 0, shade the regionbounded by these lines and x - axis. Find the area of the shaded.region.

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