MTH 251 Study Guide  Midterm Guide: Product Rule, Partial Fraction Decomposition
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15 Sep 2018
School
Department
Course
Professor
Miami University
MTH 251
Calculus II
Winter 2018
Term Test 1
Professor: Konstantinos Beros
Exam Guide
Table of content:
 Review
 Section 7.2: Trigonometric Integrals
 Section 7.3: Trigonometric Substitution
 Section 7.4: Partial Fractions
 Section 7.8: Improper Integrals
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