Given
n= 4equal-width rectangles
[tex]\int ^2_{-2}f(x)=\int ^2_{-2}(x^3+8)dx[/tex]
To determine the height of each rectangle.
Now,
The right end point of each sub-interval is 2.
Let f(x) be the height of the rectangle.
therefore, for the rectangle bases is 1 in each case.
That implies the value of x in each integrand is, 2,1,0,-1,-2.
Then,
For x=2,
[tex]\begin{gathered} f(2)=2^3+8 \\ =8+8 \\ =16 \end{gathered}[/tex]
For x=1,
[tex]\begin{gathered} f(1)=1^3+8 \\ =1+8 \\ =9 \end{gathered}[/tex]
For x=0,
[tex]\begin{gathered} f(0)=0^3+8 \\ =8 \end{gathered}[/tex]
For x=-1,
[tex]\begin{gathered} f(-1)=(-1)^3+8 \\ =-1+8 \\ =7 \end{gathered}[/tex]
For x=-2,
[tex]\begin{gathered} f(-2)=(-2)^3+8 \\ =-8+8 \\ =0 \end{gathered}[/tex]
Hence, the height of each rectangle is,
