Approximating the Area Under a Curve Using the Midpoint Method Introduction The signed area A between the curve y=f(x) and the x-axis from a to b can be approximated by summing the individual areas of n equal-width rectangles according to the formula: A~~A_(n)= sum_(i=1)^n f(x_(i)) Delta x=(f(x_(1))+f(x_(2))+cdots+f(x_(n))) Delta x where Delta x= solutionspile.com

Question

Approximating the Area Under a Curve Using the Midpoint Method Introduction The signed area

A

between the curve

y=f(x)

and the

x

-axis from

a

to

b

can be approximated by summing the individual areas of

n

equal-width rectangles according to the formula:

A~~A_(n)=\sum_(i=1)^n f(x_(i))\Delta x=(f(x_(1))+f(x_(2))+cdots+f(x_(n)))\Delta x

where

\Delta x=(b-a)/(n) and x_(i)=a+(2i-1)/(2)\Delta x, so 
x_(1)=a+(\Delta x)/(2),x_(2)=a+(3\Delta x)/(2),dots,x_(n-1)=a+(2(n-1)-1)/(2)\Delta x,x_(n)=b-(\Delta x)/(2)

This method for obtaining the approximated area

A_(m)

is referred to as the Midpoint Method, as the heights of the rectangles are determined by the function value at the midpoint of each rectangle. A depiction of the Midpoint Method with 10 rectangles is provided below for

f(x)=x^(2)

on

0,1

:

Accepted Answer

Expert Answer to -  Approximating the Area Under a Curve Using the Midpoint Method Introduction The signed area A betwe

Answer

Solution for -  Approximating the Area Under a Curve Using the Midpoint Method Introduction The signed area A betwe

Answer

This an additional answer to -  Approximating the Area Under a Curve Using the Midpoint Method Introduction The signed area A betwe

(Solved): Approximating the Area Under a Curve Using the Midpoint Method Introduction The signed area A betwe ...

View Expert Answer

Expert Answer

Buy This Answer $5

Place Order

We Provide Services Across The Globe