Constant and a variable in a squareroot needs integrating

[ferrelhadley]

Homework Statement

[URL]http://s39.photobucket.com/albums/e178/dorlomin/enviroment/?action=view&current=core2.jpg[/URL]
http://s39.photobucket.com/albums/e178/dorlomin/enviroment/?action=view&current=core2.jpg"

Homework Equations

In the question shown the equation is required to be integrated to apply the trapezium rule. However the x(20-x)^1/2 is confusing me somewhat.

The Attempt at a Solution

When I attempt the question the only way I can think of doing it is be multiplying the 'x' onto the '(20-x)^1/2'
But the resultant I get is
(4.47x - x^3/2)

The get 4.47/2x^2 - 2/5x^5/2

Can anyone point me to a worked example of how to deal with a constant and a variable in a squareroot?

My solutions is not giving me the right answers...

 

[Char. Limit]

From what I can tell, you'd be greatly helped by the substitution u=20-x, du=-dx. Then rewrite x as 20-u to get -(20 - u) u^1/2 du.

 

[SteamKing]

If you read the problem statement carefully, you are instructed first to fill out the missing depth values in the table. Did you do that?

Once the table is complete, then you are to calculate the cross sectional area of the river channel by using the trapezoidal rule for numerical integration. Do you understand what the trapezoidal rule is and how it is applied?

Once you have calculated the cross sectional area, you are given a current velocity for the water flowing in the channel and asked to estimate the flow rate of the water.

The problem does not ask you to integrate the depth function analytically to find the cross sectional area of the channel. Instead, you are supposed to calculate area numerically using the trapezoidal rule.

 

[ferrelhadley]

Do you understand what the trapezoidal rule is and how it is applied?

I did not but have now found out and found the missing values
1.6 3.2 and applied the trapezoid formula and gotten 43.86

Many thanks