. N=n => width = 1/n US = =1/n3[1+4+9+….+n2] US =

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Presentation transcript:

. N=n => width = 1/n US = =1/n3[1+4+9+….+n2] US =

=

Definite Integral We will define to be the limit as n approaches oo of where Dxi = (b-a)/n and is any point in the ith interval.

where Dxi = (b-a)/n and is any point in the ith interval, [xi-1,xi].

> 0 when f(x) > 0, but it is negative when f(x)<0. We will define to be the limit as n approaches oo of and is any point in the ith interval, [xi-1,xi].

Definition Theorems 1. 2. 3. 4.

Definition Theorems 5. 6. 7. 8.

If f(x) >= 0 on [a,b] then is the area under f(x) and over the x-axis between a and b.

If f(x) <= 0 on [a,b] then is the negative of the area over f(x) and under the x-axis between a and b.

[

[ 0.50 0.1

[

[ 2.0 0.1

]

] 0.0 0.1

[

[

[ 1.0 0.1

[

[ 1.5 0.1

]

] 1.0 0.1

where Dxi = (b-a)/n and is any point in the ith interval, [xi-1,xi]. If the interval is [-4, 4] evaluate 8p

Pi = 3.14

Pi = 3.14 6.28 0.1

Pi = 3.14

Pi = 3.14 -6.28 0.1