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
Q

substitution for a^2 - x^2

A

asin(theta)

2
Q

substitution for a^2 + x^2

A

atan(theta)

3
Q

substitution for x^2 - a^2

A

asec(theta)

4
Q

tan^2 x

A

sec^2 x - 1

5
Q

sec^2 x

A

tan^2 x +1

6
Q

integral of tan(x)

A

ln|sec x| +C

7
Q

integral of sec(x)

A

ln|sec x+ tan x|+C

8
Q

integral of tan^2(X)

A

tan x - x +C

9
Q

integral of tan^4(X)

A

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

10
Q

double angle sin(2x)

A

2sinXcosX

11
Q

double angle cos(2x)

A

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

12
Q

d/dx 2^n

A

ln(2)*2^n

13
Q

Direct Comparison Test for Convergence

A

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

14
Q

Direct Comparison Test for Divergence

A

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