Write the summation to estimate the area under the curve y = 1 + x2 from x = -1 to x = 2 using 3 rectangles and right endpoints

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

step-by-step explanation:

i hope this is what you were looking for.

see attached graph