Question

Use the mid-point rule with n=4 to approximate the area of the region bounded by y=-x^3 and y=-x

Answer 1

Given the following question:

Formula for midpoint:

`D=-x-(-x^3)=x^3-x`

Four regions:

x = -1 to x = -0.75

Which gives us...

-0.875

x = -0.75 to x = -0.5

= -0.625

x = -0.25 to x = 0

= -0.125

x = -0.5 to x = -0.25

= -0.375

Substitute the values in the formula given:

`\begin{gathered} D=-x-(-x^3)=x^3-x \\ -0.875^3+0.875=0.205078 \\ -0.625^3+0.625=0.380859 \\ -0.375^3+0.375=0.322266 \\ -0.125^3+0.125=0.123047 \\ 0.205078+0.380859+0.322266+0.123047*0.25 \\ 0.205078+0.380859+0.322266+0.123047=1.03125 \\ 1.03125*0.25=0.257 \\ =0.257 \end{gathered}`