26-4-15

Find centroid of region bounded by following curves:

y = 4x^2

y = 2x^3

I found two y intercepts: x = 2 and x = -2

obvious x intercept is zero

Attempt:

A = (int) 2x^3 - 2x^2

boundary 0 and 2

1/2x^4 - 2/3x^3 =

1/2(2^4) - 2/3(2^3) = 8 - 2.666 = 5 1/3

X centroid:

1/2 * 1/(5.333) (int) [(2x^3)^2 - (4x^2)^2]

boundaries 2 and -2

= .09375 (int) 4/7x^7 - 16/5x^5

plugging in 2

= 4/7(2^7) - 16/5(2^5) = -29.26

completely wrong... so where'd I go wrong? Thanks