trapezodial rule

[mr.burger]

Sketch a graph of x= y^(1/2)
Use the trapezoidal rule with 6 trapezoids to approximate the area bounded by this graph, the x-axis and the line x=1 and x=3. Compare your results with the actual area.

 

[Gene]

The trapazoid rule is
A = (b-a)/n*{.5(y₁ + y_n+1) + sumy_{2 to n}(y_a)
y = x^2
The steps are 1/3
y₁) = (1)^2 = 1
y₂) = (4/3)^2 = 16/9
y₃) = (5/3)^2 = 25/9
y₄) = (6/3)^2 = 36/9
y₅) = (7/3)^2 = 49/9
y₆) = (8/3)^2 = 64/9
y₇) = (9/3)^2 = 9
A = (3-1)/6*.5*(1+9)+(16+25+36+49+64)/9