The area of each rectangle is its width times its height, so the total area is:
3/4*f(0)+3/4*f(3/4)+3/4*f(3/2)+3/4*f(9/4)
3/4*1 + 3/4*25/16+3/4*13/4+3/4*97/16=285/32 = 8.906
-First I need to know how the multiplied fractions were arrived at from the first line to the second line. -What I mean is how did he get 25/16 from the second multiplied fraction(top line). And then I need to know how the second line was worked out. I appreciate this greatly.
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Sorry about that. Problem pertains to using Riemann sums just by using fractions and not involving complex formulas containing sigma signs.
In the example it states to the approximate the area beneath the curve f(x) = x^2 + 1 on the interval [0,3] using a left Riemann Sum with four rectangles.
The width of each area:
deltax = 3 - 0
------ = 3/4
4
-the rectangles being defined by the following intervals:
[0,3/4],[3/4,3/2],[3/2,9/4] and [9/4,3]. The area then calculated using the formula from above.
In the example it states to the approximate the area beneath the curve f(x) = x^2 + 1 on the interval [0,3] using a left Riemann Sum with four rectangles.
The width of each area:
deltax = 3 - 0
------ = 3/4
4
-the rectangles being defined by the following intervals:
[0,3/4],[3/4,3/2],[3/2,9/4] and [9/4,3]. The area then calculated using the formula from above.
lfje Jul 14, 2010
I know nothing about calculus. Hopefully someone else in the group can pick this up and offer some help. Sorry.
Rob Jul 14, 2010
I passed your question to a friend who is an engineer with a good working knowledge of calculus. As soon as I get an answer from him I'll put it up.
Rob Jul 14, 2010
