Wednesday

April 1, 2015

April 1, 2015

Posted by **travis** on Sunday, November 28, 2010 at 10:35pm.

- calculus -
**MathMate**, Monday, November 29, 2010 at 9:45amThe expression x²-12x crosses the x-axis twice, at x=0 and x=12.

The curve stays below the x-axis on the interval [0,12].

See:

http://img207.imageshack.us/img207/3690/1291001724centroid.png

The area is therefore:

I1=∫(x^2-12x)dx from x=0 to x=12.

By symmetry, the centroid lies on the line x=6.

To find the y-distance, evaluate the integral in which each slice is multiplied by y/2=(x^2-12x), equal to the centroid of each slice:

I2=∫(1/2)(x^2-12x)²dx

The y-position of the centroid is then:

yc=I2/I1

I get yc=-14.4 (below the x-axis)

**Answer this Question**

**Related Questions**

calculus - could some body please check this for me? 1. find the exact ...

Calculus - Find the centroid of the region bounded by the curve sin x on the ...

Calculus - Hi, I need someone to double check my answer because it doesn't seem ...

Math61 - R is bounded by Y=2x-x^2 and the x-axis. Find the centroid of R. Sketch...

Calculus - 1. Find the area of the region bounded by the curves and lines y=e^x ...

calculus - 3). The shaded region is bounded by the y-axis and the graphs of y=1...

calculus - find the centroid of the plane region bounded by the curves y = cos x...

calculus - Find the coordinates of the centroid of the following volume of ...

calculus - A region is bounded by the function y=2x^2+3 and the x-axis over the ...

calculus - The figure shows the region bounded by the x-axis and the graph of . ...