How do you use the trapezoidal rule with n=2 to approximate the area under the curve #y=1/x^2# from 1 to 3?

1 Answer
Jul 15, 2015

Answer:

Draw 2 trapezoids under the curve, the first between #x=1# and #x=2# and the second between #x=2# and #x=3#; use the sum of the areas to approximate the required area.

Explanation:

With #n=2# we have 2 trapezoids
The first will have a width of #1# (the distance on the X-axis between 1 and 2)
and an average height of #(1/1^2 + 1/2^2)/2 = 5/8#

The second will also have a width of #1# (the distance between 2 and 3)
and will have an average height of #(1/2^2+1/3^2)/2 = 13/36#

The total area of the two trapezoids (approximating the area under the curve) is
#color(white)("XXXX")##5/8 + 13/36 = (45+26)/72 = 71/72#

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