Studied by 10 peoplekseniya and i are besties forever
dy/dx sin x
= cos x
dy/dx cos x
= -sin x
dy/dx tan x
= sec^2(x)
dy/dx cot x
= -csc^2(x)
dy/dx sec x
= sec x tan x
dy/dx csc x
= csc x cot x
∫ sin x dx
= -cos x + C
∫ cos x dx
= sin x + C
∫ tan x dx
= ln |sec x| + C
∫ cot x dx
= ln |sin x| + C
∫ sec x dx
= ln |sec x + tan x| + C
∫ csc x dx
= ln |csc x + cot x| + C
∫ 1/x dx
= ln |x| + C
cos(2x)
= cos^2(x) - sin^2(x)
cos^2(x) + sin^2(x)
= 1
sin (2x)
= 2 sin x cos x
cos^2(x)
= 1 - sin^2(x)
cos^2(x)
= (1+cos2x) / 2
sin^2(x)
= 1 - cos^2(x)
sin^2(x)
= 1 - cos (2x) / 2
∫ e^kx dx
= e^kx / k + C
∫ sec^2(x)
= tan x + C
∫ csc^2(x) dx
= -cot x + C
∫ csc x cot x dx
= -csc x + C
1 + cot^2(x)
= csc^2(x)
tan^2(x) + 1
= sec^2(x)
What trig substitution does √(a^2 - x^2) belong with ? What is it's identity?
x = a sin θ; 1 - sin^2(x) = cos^2(x)
What trig substitution does √(a^2 + x^2) belong with ? What is it's identity?
x = a tan θ; 1 + tan^2(x) = sec^2(x)
What trig substitution does √(x^2 - a^2) belong with ? What is it's identity?
x = a sec θ; sec^2(x) - 1 = tan^2(x)
How do you tell if a function is convergent?
The answer to the integral is a finite number.
How can you tell if a function is divergent?
The answer to the integral is an infinite number (infinity).
What is the integration by parts formula?
∫u dv = uv - ∫v du
Note
Flashcard