Use definition 2 to find an expression for the area under the graph of as limit.

Amari Flowers

Amari Flowers

Answered question

2021-10-15

To get an expression for the region under the graph of as limit, use definition 2. Avoid evaluating the boundary.
f(x)=2xx2+1,1x3

Answer & Explanation

Raheem Donnelly

Raheem Donnelly

Skilled2021-10-16Added 75 answers

The second definition says that
Area =limnxi=1nf(xi) 
Where x=ban 
If we choose xi as the right end point of each interval, then 
Area =limbxi=1nf(a+ix) 
In this problem 
f(x)=2xx2+1 
a=1,b=3 
Hence x=ban=31n=2n 
Area =limnxi=1nf(a+ix)=limn2ni=1nf(1+i2n) 
=limn2ni=1n2[1+2in][1+2in]2+1 
Result: limn2ni=1n2[1+2in][1+2in]2+1

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