Final Exam: Cheat Sheet" [PDF]

Final Exam: Cheat Sheet". 1. Z. 1 x dx = lnjxj. 2. Z ax dx = ax lna. 3. Z sinx dx = ,cosx. 4. Z cos x dx = sinx. 5. Z se

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Idea Transcript


7/17/97

Final Exam: \Cheat Sheet" 1. 2. 3. 4. 5.

Z

1 dx = ln jxj x ax ax dx = lna

Z Z Z Z

cos x dx = sin x

9.

sec x dx = tanx

10.

13. Cylindrical Shells: V = b a

Z

8.

Z

b a

Z

a

b

csc x cot x dx = , csc x dx = 1 tan,  x  x +a a a x dx p = sin, a a ,x 1

Z

2

2

1

2

2

Z

b a

Z

d

c

[f(y) , g(y)] dy Z

[f(x)] dx. Around the y-axis: V =

d

2

c

[g(y)] dy 2

2xf(x) dx where 0  a < b

f(x)g0 (x) dx = f(x)g(x)]ba , R

Z

sec x tan x dx = sec x

[f(x) , g(x)] dx. In terms of y: A =

12. Volume around the x-axis: V =

14.

Z

sin x dx = , cos x

11. Area in terms of x: A =

csc x dx = , cot x 2

7.

2

Z

Z

6.

Z

b

f 0 (x)g(x) dx

a m n sin x cos x dx.:

15. How to Evaluate If m or n are odd use sin x = 1 , cos x and cos x = 1 , sin x, respectively and then apply substitution. Otherwise, use sin x = (1,cos 2x) or cos x = (1+cos 2x) or sin x cos x = sin 2x. R 16. How to Evaluate tanm x secn x dx.: If m is odd or n is even, use tan x = sec x , 1 and sec x = 1 + tan x, respectively and then apply substitution. 17. Table of Trigonometric Substitutions Expression Substitution Identity p    a , x x = a sin, , 1 , sin  = cos  p 

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