Draw the area enclosed by the curves, and estimate the position of the center of...

Kathy Williams

Kathy Williams

Answered

2021-12-21

Draw the area enclosed by the curves, and estimate the position of the center of gravity.
y=ex, y=0, x=0, x=5
Determine the precise coordinates of the centroid
(x,y)=

Answer & Explanation

Thomas Nickerson

Thomas Nickerson

Expert

2021-12-22Added 32 answers

Consider the following curves:
y=f(x)=ex, y=0, x=0, x=5
Find the exact coordinates of the centroid
Calculate the total are as follows:
A=abf(x)dx
=05exdx
=(ex)05
=e51
Raymond Foley

Raymond Foley

Expert

2021-12-23Added 39 answers

Calculate the y-coordinates of the centroid as follows:
y=MxA
Here Mx=12abf2(x)dx
=1205(ex)2dx
=1205e2xdx
=12(e2x2)05
=14(e101)
Then, y=MxA
=14(e101)e51
=14×(e5)212e51
=14×(e51)(e5+1)e51
=14(e5+1)
37.35

RizerMix

RizerMix

Expert

2021-12-29Added 437 answers

Calculate the x-coordinates of the centroid as follows:
x=MyA
Here My=abxf(x)dx
=05xexdx
=5e5e5+1
4e5+1
Then, x=MyA
4e5+1e51
4.0

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