Find the centroid of the region bonded by the line y=x and the parabola y=x2?
- PopeLv 74 weeks ago
You must mean y = x and y = x², right? Similar problems come up so often that it may be worth your trouble to learn this geometric property of parabolas.
The region you defined is a parabola segment.
Its chord joins O(0, 0) and A(1, 1).
The midpoint of the chord is B(1/2, 1/2).
The central diameter is the line parallel to the axis and bisecting the chord.
central diameter: x = 1/2
The central diameter meets the parabola at C(1/2, 1/4).
The centroid, K, lies on the central diameter, dividing BC internally in ratio 2:3.
y-coordinate of K
= [3(1/2) + 2(1/4)] / (2 + 3)
- rotchmLv 74 weeks ago
Hint: First you need to know the concept, or formulas, for the centroid. State them here and we will proceed to show you how to apply them to your problem.
x_c = ?
y_c = ?