Calculus Formulas

Question 1

Integral of sec(x)tan(x) dx

Answer 1

sec(x) +c

Question 2

Integral of sec^2(x) dx

Answer 2

tan(x) +c

Question 3

Integral of cosec^2(x) dx

Answer 3

-cot(x) +c

Question 4

Integral of tan(x) dx

Answer 4

ln|sec(x)| +c

Question 5

Integral of cot(x) dx

Answer 5

ln|sin(x)| +c

Question 6

Integral of sec(x) dx

Answer 6

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

Question 7

Integral of cosec(x) dx

Answer 7

-ln| cosec(x) +cot(x)| + c

Question 8

Integral of 1/(a^2 -x^2)^(1/2) dx

Answer 8

arcsin(x/a) +c

Question 9

Integral of 1/(a^2 -x^2) dx

Answer 9

1/a arctan(x/a) +c

Question 10

Integral 1/|x| (x^2 -a^2)^(1/2)

Answer 10

1/a arctic(x/a) +c

Question 11

Sin(A+/-B) =

Answer 11

SinACosB +/- SinBCosA

Question 12

Cos(A+/-B) =

Answer 12

CosACosB -/+ SinASinB

Question 13

Sin(2A) =

Answer 13

2Sin(A)Cos(A)

Question 14

Cos(2A)=

Answer 14

Cos^2(A) -Sin^2(A)
2Cos^2(A) -1
1-2Sin^2(A)

Question 15

Formula linking Cos^2 and Sin^2

Answer 15

Cos^2+Sin^2 =1

Question 16

Formula linking Sec^2 and tan ^2

Answer 16

Sec^2=1+ tan^2

Question 17

Cosh(x)

Answer 17

(e^x +e^-x)/2

Question 18

Sinh(x)

Answer 18

(e^x-e^-x)/2

Question 19

What are the two trig angle triangles

Answer 19

1. 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.
2. Right angle triangle with two angles pi/4. Sides are 1,1 and hypotenuse is root 2

Question 20

Integral of f’(x)/f(x) dx =

Answer 20

ln|f(x)| +c

Question 21

Odd and even functions
f(-x) =
f(-x)=

Answer 21

f(x) even function

-f(x) Odd function

Question 22

Volume of revolution

Answer 22

V= pi x integral from a to b of y^2 dx

Question 23

Arc length

Answer 23

L = Integral from a to b of sqrt(1+ (y’)^2) dx

Question 24

Area of revolution

Answer 24

A= 2pi x integral from a to b of [y x sqrt(1+ (y’)^2) dx]

Question 25

Taylor Polynomials and Mauclaurin Polynomials

Answer 25

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)