Trig Substitutions and Important Integrarls Flashcards Preview

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Flashcards in Trig Substitutions and Important Integrarls Deck (14)
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1

substitution for a^2 - x^2

asin(theta)

2

substitution for a^2 + x^2

atan(theta)

3

substitution for x^2 - a^2

asec(theta)

4

tan^2 x

sec^2 x - 1

5

sec^2 x

tan^2 x +1

6

integral of tan(x)

ln|sec x| +C

7

integral of sec(x)

ln|sec x+ tan x|+C

8

integral of tan^2(X)

tan x - x +C

9

integral of tan^4(X)

(1/3) tan^3(x) -tan x +x +C

10

double angle sin(2x)

2sinXcosX

11

double angle cos(2x)

Cos^2 X - sin^2 X
Or
1-2sin^2 X

12

d/dx 2^n

ln(2)*2^n

13

Direct Comparison Test for Convergence

0<=g(x); f(x) converges if g(x) converges

14

Direct Comparison Test for Divergence

0<=f(x),+g(x); g(x) diverges if f(x) diverges