find the area enclosed by the curve y=x with x-axis and x=1 using determinants
Answers
Given : area enclosed by the curve y=x with x-axis and x=1
To Find : Area
Solution:
y = x
x -axis => y = 0
x = 1
y = x & y = 0
=> (0 ,0) is the point
y = x and x = 1
=> ( 1 , 1) is the point
y = 0 , x = 1
=> (1 , 0) is the point
(0 , 0) , (0 , 1) , ( 1, 1)
=> A = (1/2) | 0 ( 1 - 1) - 0(0 - 1) + 1 (0 - 1) |
=> A = (1/2) | - 1|
=> A = 1/2
area enclosed by the curve y=x with x-axis and x=1 is 1/2 sq units
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FORMULA TO BE IMPLEMENTED
If the vertices of a triangle ABC is
Area of the triangle ABC is
TO DETERMINE
The area enclosed by the curve y=x with x-axis and x=1 using determinants
CALCULATION
We first find the points of intersection of the line with coordinate axis
For the point of intersection of the line y = x and x = 1
So the point of intersection is ( 1, 1 )
So the vertices of the triangle OAB are
The shaded region is bounded by the line y = x, x axis and x = 1
So by the determinant method the area of the Triangle OAB is
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