Section 28.8 No. 5
I=
by using the substitution x= tan
Then this expression can be reduced to: this integral
Is of the form with
We finally get the answer: I= that is I =
From our substitution we can get the following relation:
x= tan and it corresponds t

Integration by Parts:
If you have a function that you want to integrate and it is a combination of 2 functions:
u and v , we are going to use a property of derivatives to obtain the formula for integration
by parts:
since:
multiplying both sides by dx:
we

Approximation Methods
of integration
x
2
2.5
3
3.5
4
AT =
Simpson
y=sqrt(x2-1)
1.7320508076
2.2912878475
2.8284271247
3.3541019662
3.8729833462
Total Area
5.6405746097
(0.5/3)*(B2+4*(B3)+2*(B4)+4*(B5)+(B6)
Notice the difference of the 2 formulas used.
AT

Week 2 Trigonometric integrations:
Hint to solve:
Expand the binomial:
you get 3 integrals :
Use the fact that to integrate each of the terms
where u = tan x and du = secxdx
the last 2 are now of the form

Ex. 9
x
Please, click on cell B6 to see the formula used
you can also see the formulas used for each of the terms obtained in column C
since n= 5 then h= 1
f(x)
Terms
0
5
5
1 4.898979 9.797959
2 4.582576 9.165151
3
4
8
4
3
6
5
0
0
sum: 37.96311
Then the i

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Visits to COLL148 by Campus/Center Resources
You should contact these resources to schedule visitsif they havent already contacted you within the first two weeks of the session.
Suggested
Visit Date
Resource
Week 2
Financial Literacy Consultant Financial