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?

Aug 30, 2015

Answer:

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
${A}_{i} = \frac{f \left({x}_{i}\right) + f \left({x}_{i + 1}\right)}{2} \cdot w i \mathrm{dt} h$
$\textcolor{w h i t e}{\text{XXXXXXXX}}$ where $w i \mathrm{dt} h$ is the width of each strip (i.e. $\frac{2}{20} = 0.1$)

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: