MTH 251 Study Guide - Midterm Guide: Product Rule, Partial Fraction Decomposition

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Miami University
MTH 251
Calculus II
Winter 2018
Term Test 1
Professor: Konstantinos Beros
Exam Guide
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Table of content:
- Review
- Section 7.2: Trigonometric Integrals
- Section 7.3: Trigonometric Substitution
- Section 7.4: Partial Fractions
- Section 7.8: Improper Integrals
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-To find u, look for a function who’s
derivative is also in the function
Review
Substitution Review
If u=g(x) is differentiable, then
()()=() if u=g(x) and du=g’(x)
Example a:
 ()
()
u=cos(2x)
du=-2sin(2x)dx
Solving so that cancellation is possible:
-
= sin(2)
Plugging in to the integral:
1
21
1 + 
Solving this Integral:
-
arctan()+
Plugging u back in:
=
arctan(cos(2)) +
-Because -2sin(2x) is also in the
function, without the -2
arctan () = tan
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