Question

How do you use the trapezoidal rule with n=10 to approximate the area between the curve `1/sqrt(1+x^3)` from 0 to 2?

Answer 1

Area is approximately `2.09`

Explanation:

Divide the range `0` to `2` into `20` vertical strips at points `x_0:x_20` along the X-axis.

Calculate the value of `f(x_i) = 1/(sqrt(1+x_i^3)` for each point.

Calculate the area of each trapezoidal strip as
`A_i = (f(x_i)+f(x_(i+1)))/2 * width`
`color(white)("XXXXXXXX")` where `width` is the width of each strip (i.e. `2/20 = 0.1`)

Sum the area of all the trapezoidal strips to get an approximation of the integral.

Theoretically this could be done by hand (if you need the arithmetic practice) but I chose to use a spreadsheet: