## USING METHOD OF INTEGRATION ,HOW TO FIND AREA OF TRIANGLE BOUNDED BY THREE LINES

Using method of integration find the area of triangle,using the method of integration find the area of the region bounded by the lines,area of triangle by integration method

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**Using Method of Integration , How to find the area of triangle bounded by three lines **

2x + y = 0 , 3x - 2y = 6 and x - 3y + 5 = 0##
**Solution**

Given lines are

3x - 2y = 6 --------- (2) and

x - 3y = -5 --------- (3)

If these lines are intersecting then we have to find their coordinates of points of intersection .

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To Find Coordinate of Point A

Multiply (1) by 2 and adding to (2) , we get4x + 2y + 3x - 2y = 8 + 6

7x = 14 ⇒ x =2

Putting x = 2 in (1) , we get

Area under Curve |

4 + y = 4 ⇒ y = 0

∴ (1) and (2) meets at point A(2,0).

### To Find Coordinate of Point B

To find point of intersection (2) and (3);Multiply (3) by -3 and adding to (2) , we get

3x - 2y -3x +9y = 6 +15

7y = 21 ⇒ y = 3

Putting y = 3 in (3) , we get

x-3(3) = -5

⇒ x = -5 +9 ⇒ x = 4

∴ (2) and (3) meets at point B(4,3).

### To Find Coordinate of Point C

To find point of intersection (1) and (3);Multiply (1) by 3 and adding to (3) , we get

6x + 3y + x - 3y = 12 - 5

7x = 7 ⇒ x =1

Putting x = 1 in (1) , we get

2(1) + y = 4

⇒ y =4 - 2 ⇒ y = 2

∴ (1) and (3) meets at point C(1,2).

we get points of intersection of (1) and (2) A(2,0), points of intersection of (2) and (3) B(4,3) and points of intersection of (1) and (3) C(1,2).

## Required Area = Shaded Area = Area DCBED - Area DCAD -Area ABEA

**Also read my previous post**

**How to find area bounded by two circles**

For better understanding watch this video

## Conclusion

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