Find the area bounded by the curve y=x x-axis and the ordinates x=0,x=4
Answers
Answer:
Step-by-step explanation:
Answer:
8 square units
Step-by-step explanation:
Concept= Area under the curve
Given= The curve and coordinate
To find= The area bounded by curve
Explanation=
We have been given to find the area bounded by the curve y=x x-axis and the ordinates x=0,x=4.
Curve: y=x
Since the curve is a straight line passing from the coordinates (0,0) and is plotted with equal value of x and y.
To find the area bounded by the curve we integrate the curve with the coordinates as a definite integral.
Example: Curve is given as m=n and the coordinates whose under area is to be found is a,b. Here a is the smaller one and b greater.
Area: m=ᵇ∫ₐ n dn square units, this gives the area.
Here curve is y=x and the coordinates are x=0 and x=4.
So we need to find the area bounded by the curve between x=0 and x=4.
Definitely it will be triangle with base 4 and height 4.
Area according to formula=
y= ⁴∫₀ xdx
y= ⁴[x²/2]₀ = 4²/2 - 0²/2 = 4²/2 = 16/2 = 8 square units.
The same result we get as triangle area is 1/2 *base*height = 1/2 *4 * 4 = 8
Therefore the area bounded by curve is 8 square units.
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