Calculus I: Find the area under the curve using the following methods...
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Calculus I: Find the area under the curve using the following methods...

[From: ] [author: ] [Date: 12-04-02] [Hit: ]
Change in x(f(1.125)+f(1.375)+f(1.625)+f(1.......
find the area under the curve y=2x-x^2 from x=1 to x=2 with n=4 using
a.) inscribed rectangles
b.) circumscribed rectangles
c.) the trapezoid rule
d.) Midpoint formula

The problem is that I dont remember, so could someone just remind me of the formulas and then explain a little on how to apply them to this situation? No need to show work.
Thanks!

-
To find the width of your rectangles it's b-a/n so 2-1/4 1/4.The width is 1/4 per rectangle

I DRUL stands for Inscribed down right up left.Talking about concavity

so 2x-x^2=y
2-2x=y'
-2=y'
this is concave down so they are on the right for inscribed

so
a) change in x(f(1.25)+f(1.5)+f(1.75)+f(2))

b)Circumscribed wil be on left
change in x(f(1)+f(1.25)+f(1.5)+f(1.75))

c) h/2 (f(1)+2f(1.25)+2f(1.5)+2f(1.75)+f(2))

d)Midpint

Change in x(f(1.125)+f(1.375)+f(1.625)+f(1.875)
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