Answer:
The estimated area is 8 square units.
Step-by-step explanation:
y=f(x)=1+x²
Left point: a=x=-1
Right point: b=x=2
Range: r=b-a→r=2-(-1)→r=2+1→r=3
Width of each of the 3 equal rectangles: w=r/3→w=3/3→w=1
First right endpoint is x1=a+w→x1=-1+1→x1=0
Second right endpoint is x2=x1+w→x2=0+1→x2=1
Third right endpoint is x3=x2+w→x3=1+1→x3=2
Estimated Area: A≈A1+A2+A3
A1=w*f(x1)→A1=w*f(0)
x=0→f(0)=1+0²→f(0)=1+0→f(0)=1
A1=w*f(0)→A1=1*1→A1=1
A2=w*f(x2)→A2=w*f(1)
x=1→f(1)=1+1²→f(1)=1+1→f(1)=2
A2=w*f(1)→A2=1*2→A2=2
A3=w*f(x3)→A3=w*f(2)
x=2→f(2)=1+2²→f(2)=1+4→f(2)=5
A3=w*f(2)→A3=1*5→A3=5
A≈A1+A2+A3→A≈1+2+5→A≈8 square units
