The trapezoidal approximation will be the average of the left- and right-endpoint approximations.
Let's consider a simple example of estimating the value of a general definite integral,

Split up the interval 
![[a,b]](https://tex.z-dn.net/?f=%5Ba%2Cb%5D)
 into 

 equal subintervals,
![[x_0,x_1]\cup[x_1,x_2]\cup\cdots\cup[x_{n-2},x_{n-1}]\cup[x_{n-1},x_n]](https://tex.z-dn.net/?f=%5Bx_0%2Cx_1%5D%5Ccup%5Bx_1%2Cx_2%5D%5Ccup%5Ccdots%5Ccup%5Bx_%7Bn-2%7D%2Cx_%7Bn-1%7D%5D%5Ccup%5Bx_%7Bn-1%7D%2Cx_n%5D)
where 

 and 

. Each subinterval has measure (width) 

.
Now denote the left- and right-endpoint approximations by 

 and 

, respectively. The left-endpoint approximation consists of rectangles whose heights are determined by the left-endpoints of each subinterval. These are 

. Meanwhile, the right-endpoint approximation involves rectangles with heights determined by the right endpoints, 

.
So, you have


Now let 

 denote the trapezoidal approximation. The area of each trapezoidal subdivision is given by the product of each subinterval's width and the average of the heights given by the endpoints of each subinterval. That is,

Factoring out 

 and regrouping the terms, you have

which is equivalent to

and is the average of 

 and 

.
So the trapezoidal approximation for your problem should be 
 
 
        
        
        
2S/7 2 shaded out of 7 circles
        
             
        
        
        
The answer is X = 5 because first you have to take away 2x from that side so u minus 2x from 4x that gives u: 72 + 2x = 82 then you have to minus 72 from both sides and that gives you 2x = 10 once you have that you divide both sides by 2 because you want the X by itself and once you get that X = 5. Hope this helped!
        
                    
             
        
        
        
X + x + 1 + x + 2 + x + 3 = 330
4x + 6 = 330
4x = 324, x = 81
Smallest number: 81
Biggest number: 81 + 3 = 84
Sum: 81 + 84 = 165
The answer is 165