1 Answer

Faultier · Answer 1 · 2023-12-12T10:23:17+0000

Given

n= 4equal-width rectangles

$\int ^2_(-2)f(x)=\int ^2_(-2)(x^3+8)dx$

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,

$\begin{gathered} f(2)=2^3+8 \\ =8+8 \\ =16 \end{gathered}$

For x=1,

$\begin{gathered} f(1)=1^3+8 \\ =1+8 \\ =9 \end{gathered}$

For x=0,

$\begin{gathered} f(0)=0^3+8 \\ =8 \end{gathered}$

For x=-1,

$\begin{gathered} f(-1)=(-1)^3+8 \\ =-1+8 \\ =7 \end{gathered}$

For x=-2,

$\begin{gathered} f(-2)=(-2)^3+8 \\ =-8+8 \\ =0 \end{gathered}$

Hence, the height of each rectangle is,

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