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Math 2414We also discuss several other topics like How do we perceive speech accurately?
Exam 1 Review
EXAM 1 REVIEW
→ TEXTBOOK CHAPTERS 6 AND 7Don't forget about the age old question of What is written and sung by harrison?
Common Integrals
Common Derivatives
Common Trig. Identities
(soh  cah  toa)
;We also discuss several other topics like If the null hypothesis were true, what is the expected value of the test statistic?
= ln sec x + tan x + C
We also discuss several other topics like What is the meaning of statuses in social structure?
+ C
ln sec x + C
Don’t forget “+C” when indefinite
If you want to learn more check out What are the 5 main characteristics of life?
 The first fundamental theorem of calculus
; where F’(x) = f(x)Don't forget about the age old question of How do the prototype approach and the exemplar approach differ from each other?
 Usubstitution: simplifies integrals so antiderivative is easier to find.
Example:
 Let u = 2t +4; du= 2 dt ⇒ dt = du/2

 (a+b) 2 = a 2 + 2 a b + b 2
 Ex. x 2 + 6 x + 4
I. Area between curves: area between the graphs of two functions (Section 6.1)
 Method I: Vertical Strips
 everything with respect to x
 Method II: Horizontal Strips
 A 1:=
 A 2 =
 everything with respect to y
II. Volume: finding the volume of a solid using an integral (Section 6.2)
 Done by “giving” the top and bottom slabs with square cross sections
 Ex: consider a solid with a base bounded by:
 y = 1x, y = 2x+5, x=0, x=3
 This is not a box, so we break it into pieces and take the limit
 Length = (2x + 5)  (1  x)
 Width = (2x+ 5)  (1 x)
 Height = Δx (we only know exact value if given)
 Volume:
 Bounds: x = (0, 3)
 Area of Cross Section: [(2 x+ 5)  (1 x)] 2
 Height: dx
 A. disk method (not square cross sections): volume generated when a region is revolved about an axis which is perpendicular to the approximating strip of the region.
 fills in the object with disks (circles with thickness) and adds them up to find volume.