Use Definition 2 to find an expression for the area under the graph of f as a li

Emily-Jane Bray 2021-10-27 Answered
Use Definition 2 to find an expression for the area under the graph of f as a limit. Do not evaluate the limit. f(x)=x2+(1+2x)12,4x7
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Expert Answer

StrycharzT
Answered 2021-10-28 Author has 102 answers
Step1
We know that,
Area=abf(x)dx=limnΔxi=1nf(a+iΔx)
Where Δx=ban
Step 2
We have
Area=47x2+1+2xdx
In this problem f(x)=x2+1+2xa=4,b=7 Hence Δx=74n=3n
Area=limn3ni=1nf(4+i3n)
Area=limn3ni=1n[(4+i3n)2+1+2(4+i3n)]
Area=limn3ni=1n[(4+3in)2+9+6in]
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