+0  
 
0
282
2
avatar

​f(x)=2x+5

a=0

b=4.

 

Approximate the area under the curve with 4 rectangles using the​ left-hand endpoint, the​ right-hand endpoint, and the midpoint. The actual area is 36. Which approximation gave the closest​ estimate?

 

Using the​ left-hand endpoint, the approximate area is ___?

 

Using the​ right-hand endpoint, the approximate area is ___?

 

And the midpoint?

Guest Apr 25, 2017
 #1
avatar+26750 
+2

Using the​ left-hand endpoint, the approximate area is f(a)*(b - a) = 5*4 → 20

 

Using the​ right-hand endpoint, the approximate area is f(b)*(b - a) = 13*4 → 52

 

Using the​ midpoint, the area is (f(a) + f(b))/2 * (b - a) = (5 + 13)/2 * 4 → 9*4 → 36

 

(Not clear why you mentioned 4 rectangles!).

Alan  Apr 25, 2017
 #2
avatar+26750 
+1

Perhaps for the midpoint I should have done f([a + b]/2)*(b - a), though, in this case, the result would be the same.

Alan  Apr 25, 2017

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