Calculus Formulas Flashcards
Integral of sec(x)tan(x) dx
sec(x) +c
Integral of sec^2(x) dx
tan(x) +c
Integral of cosec^2(x) dx
-cot(x) +c
Integral of tan(x) dx
ln|sec(x)| +c
Integral of cot(x) dx
ln|sin(x)| +c
Integral of sec(x) dx
ln|sec(x) + tan(x)| +c
Integral of cosec(x) dx
-ln| cosec(x) +cot(x)| + c
Integral of 1/(a^2 -x^2)^(1/2) dx
arcsin(x/a) +c
Integral of 1/(a^2 -x^2) dx
1/a arctan(x/a) +c
Integral 1/|x| (x^2 -a^2)^(1/2)
1/a arctic(x/a) +c
Sin(A+/-B) =
SinACosB +/- SinBCosA
Cos(A+/-B) =
CosACosB -/+ SinASinB
Sin(2A) =
2Sin(A)Cos(A)
Cos(2A)=
Cos^2(A) -Sin^2(A)
2Cos^2(A) -1
1-2Sin^2(A)
Formula linking Cos^2 and Sin^2
Cos^2+Sin^2 =1
Formula linking Sec^2 and tan ^2
Sec^2=1+ tan^2
Cosh(x)
(e^x +e^-x)/2
Sinh(x)
(e^x-e^-x)/2
What are the two trig angle triangles
- Right angle triangle with angles pi/3 in the left lower corner and pi/6 in the upper corner. Hypotenuse is length 2, right vertical length is 3 and the other is 1.
- Right angle triangle with two angles pi/4. Sides are 1,1 and hypotenuse is root 2
Integral of f’(x)/f(x) dx =
ln|f(x)| +c
Odd and even functions
f(-x) =
f(-x)=
f(x) even function
-f(x) Odd function
Volume of revolution
V= pi x integral from a to b of y^2 dx
Arc length
L = Integral from a to b of sqrt(1+ (y’)^2) dx
Area of revolution
A= 2pi x integral from a to b of [y x sqrt(1+ (y’)^2) dx]
Taylor Polynomials and Mauclaurin Polynomials
Mauclaurin - about 0
f(x) = f(0) + f’(0)x + f’‘(0) x^2/2! +…… + f^(n)x^(n)/n!
Taylor - about a
f(x) = f(a) + (x-a)f’(a) + 1/2! (x-a)^2f’‘(a) + …..+ 1/n! (x-a)^n f^(n)(a)
