Instructor: Quanlei Fang
Dept. of Math, University at Buffalo, Spring 2009
Welcome
to
Math 122 Lecture 9
Survey of Calculus and its Applications I1
!
Functions of Several Variables
!
Partial Derivatives
!
Finding Relative Maxima and Minima
!
Lagrange Multipliers and Constrained
Optimization
!
The methods of Least Squares
Chapter 9
Techniques of Integration
!
Integration by Substitution
!
Integration by Parts
!
Evaluation of Definite Integrals
!
Approximation of Definite Integrals
!
Some Applications of the Integral
!
Improper Integrals
§ 9.1
Integration by Substitution
!
Differentiation and Integration Formulas
!
Integration by Substitution
!
Using Integration by Substitution
If u= g(x), then Determine the integral by making an appropriate substitution.
x2+2x+3()6x+1()"dx
xex2"dxDetermine the integral by making an appropriate substitution. ln(tet)t"dtFind the integral
1.
x
3
1
"
x
4
#
dx
2.
1
y
2
e
1
y
#
dy
Find
the following integrals
