Find the Riemann sum of f(x) = x2-1 on [0,2] by using for subintervals of equal length and midpoint rule?

1 Answer
May 11, 2018

The answer
#S_p=1*(-3/4)+1*(5/4)=5/4-3/4=2/4=1/2=0.5#

Explanation:

these is the sketch of our function #f(x)=x^2-1#

graph{x^2-1 [-4.892, 4.974, -1.99, 2.944]}

let choice #n=2#

the width will be #width=(a-b)/n=(2-0)/2=1#

now let find the medpoint

#(0+1)/2=1/2#

#(1+2)/2=3/2#

then let find the high of the midpoint

#f(1/2)=1/4-1=(1-4)/4=-3/4#

#f(3/2)=9/4-1=[9-4]/4=5/4#

the sketch with the midpoint

Desmos.com

now we will calculate Riemann sum

#S_p=width*high#

#S_p=1*(-3/4)+1*(5/4)=5/4-3/4=2/4=1/2=0.5#