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- StudyBlue
- Washington
- Olympic College
- Mathematics
- Mathematics 152
- Heinze
- Quiz 2 Study

Jessi B.

cos^{2}(x)

1-sin^{2}(x)

tan^{2}(x)

sec^{2}(x)-1

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)

sec^{2}(x)

1+tan^{2}(x)

sin^{2}(x)

1-cos^{2}(x)

tan(x)

(normal)

opp/adj

tan(x)

(identity)

sin(x)/cos(x)

cos (x)

(normal)

adj/hyp

sin(x)

(normal)

opp/hyp

cot(x)

(normal)

adj/opp

sec(x)

(normal)

hyp/adj

csc(x)

(normal)

hyp/opp

sin^{2}(x)+cos^{2}(x)

1

(trig identity)

sin(-x)

-sin(x)

cos(-x)

-cos(x)

tan(-x)

-tan(x)

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cos(x)

(trig identity)

sin(π/2 - x)

sin(x)

(trig identity)

cos(π/2 - x)

cot(x)

(trig identity)

tan(π/2 - x)

sin^{2}(x)

(1/2)[1-cos(2x)]

cos^{2}(x)

(1/2)[1+cos(2x)]

sin(x)cos(x)

(1/2)sin(2x)

∫sin(x)dx

-cos(x) + c

∫sec^{2}(x)dx

tan(x) + c

∫sec(x)tan(x)dx

sec(x) + c

∫ 1/(x^{2}+1) dx

tan^{-1}(x) + c

∫ sinh(x) dx

cosh(x) + c

∫ (1/x) dx

ln|x| + c

∫ a^{x} dx

(a^{x}/ ln|a|) + c

∫ cos(x) dx

sin(x) + c

∫ csc^{2}(x) dx

-cot(x) + c

∫ csc(x)cot(x) dx

-csc(x) + c

∫ [1/√(1-x^{2})] dx

sin^{-1}(x) + c

∫ cosh(x) dx

sinh(x) + c

∫ tan(x) dx

ln |sec(x)| + c

∫ sec(x) dx

ln|

sec(x) + tan(x)| + c

∫ [1/(x^{2}-a^{2})] dx

(1/a)tan^{-1}(x/a) + c

f(x)= ln(x)

f'(x)=?

f'(x)= 1/x

f(x)= ?

f(x)=e^{x}

f'(x)= ?

f'(x)= e^{x}

f(x)= ?

f(x)= cos(x)

f'(x)= ?

f'(x)= -sin(x)

f(x)= ?

f(x)= sin(x)

f'(x)= ?

f'(x)= cos(x)

f(x)= ?

f(x)= tan(x)

f'(x)= ?

f'(x)= sec^{2}(x)

f(x)= ?

f(x)= csc(x)

f'(x)= ?

f'(x)=

-csc(x)cot(x)

f(x)= ?

f(x)= sec(x)

f'(x)= ?

f'(x)= sec(x)tan(x)

f(x)= ?

f(x)= cot(x)

f'(x)= ?

f'(x)= -csc^{2}(x)

f(x)= ?

work= ?

(J, ft-lb)

∫f(x) dx, a≤x≤b

f(x)= force

b-a= distance

force= ?

(N, lb_{f})

mass (times)

accelleration

Hooke's Law

F=kx

k= spring constant

x= distance from natural length

average value of a function

f_{ave}=

(1/b-a) ∫f(x) dx

a≤x≤b

∫u dv

uv- ∫ v du

∫ ln(x) dx

(x)ln|x|-x + c

∫sin^{m}(x)cos^{n}(x) dx

m= odd

use:

sin^{2}(x)=

1-cos^{2}(x)

∫sin^{m}(x)cos^{n}(x) dx

n= odd

use:

cos^{2}(x)=

1-sin^{2}(x)

∫sin^{m}(x)cos^{n}(x) dx

m & n = even

use:

half-angle identities

∫tan^{m}(x)sec^{n}(x) dx

n= even

use:

sec^{2}(x)=

1+tan^{2}(x)

∫tan^{m}(x)sec^{n}(x) dx

m= odd

use:

tan^{2}(x)=

sec^{2}(x)-1

strategy for solving integrals

1. simplify

2. obvious substitution?

3. classify: rational, trigonometric, integration by parts, radicals

4. try again...

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