Question

Find the coordinates of the centroid of the region bounded by y=12x^2 and y=3x^3. The region is covered by a thin flat plate.

Answer #1

Centroid is found using moment about axis divided by total area.

Here centroid is **(2.4, 65.83)** answer

Find the centroid of the region bounded by the graphs of the
functions y=3x^2, y=x^2+7
The centroid is at (¯x,¯y)(x¯,y¯) where

Find the centroid of the region that is bounded by the line Y =
3X, the line X = 2 and the X
axis.

Find exact coordinates of the centroid of the region bounded by
the given curves.
y = x + 30 and y = x^2

Find the centroid of the region bounded by the curves: y = 8 -
x2 , y = x2

Find the centroid of the region bounded the following curves.
Show a graph of the region.
1. ? = ? ^? , ? = ? ^−? , ? = 0, and ? = ??2.
2. ? = −? ^2 + 4? − 3 and the y-axis

find the centroid of the lamina of occupying the region bounded
by y=x,y=9

Find the centroid of the region bounded by the curve y =
x3 and x = y2
A. (3/25 , 12/7)
B. (3/7 , 12/25)
C. (12/7 , 3/25)
D. (12/25 , 3/7)

find the area of the region bounded by the graph of
y=x^3-2x^2-x+2 and y=3x^2-5x+2

In spherical coordinates, find the volume of the region bounded
by the
sphere x^2 + y^2 + z^2 = 9 and the plane z = 2.

A. For the region bounded by y = 4 − x2 and the x-axis, find
the volume of solid of revolution when the area is revolved
about:
(I) the x-axis,
(ii) the y-axis,
(iii) the line y = 4,
(iv) the line 3x + 2y − 10 = 0.
Use Second Theorem of Pappus.
B. Locate the centroid of the area of the region bounded by y
= 4 − x2 and the x-axis.

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