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?

1 Answer
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 = (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:
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