trapezodial rule

mr.burger

New member
Joined
Jun 12, 2005
Messages
21
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

Senior Member
Joined
Oct 8, 2003
Messages
1,904
The trapazoid rule is
A = (b-a)/n*{.5(y<sub>1</sub> + y<sub>n+1</sub>) + sumy<sub>2 to n </sub>(y<sub>a</sub>)
y = x^2
The steps are 1/3
y<sub>1</sub>) = (1)^2 = 1
y<sub>2</sub>) = (4/3)^2 = 16/9
y<sub>3</sub>) = (5/3)^2 = 25/9
y<sub>4</sub>) = (6/3)^2 = 36/9
y<sub>5</sub>) = (7/3)^2 = 49/9
y<sub>6</sub>) = (8/3)^2 = 64/9
y<sub>7</sub>) = (9/3)^2 = 9
A = (3-1)/6*.5*(1+9)+(16+25+36+49+64)/9
 
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