Integral Rules

Question 1

e^x

Answer 1

e^x

Question 2

1/x dx

Answer 2

ln|x|+c

Question 3

a^x dx

Answer 3

(1/lna)(a^u)

Question 4

sin x dx

Answer 4

-cos x + C

Question 5

cos x dx

Answer 5

sin x + C

Question 6

sec2 x dx

Answer 6

tan x + C

Question 7

csc² x dx

Answer 7

-cot x + C

Question 8

sec x tan x dx =

Answer 8

sec x + C

Question 9

csc x cot x dx

Answer 9

-csc x + C

Question 10

tan x dx

Answer 10

-ln |cos x| + C

Question 11

cot x dx

Answer 11

ln |sin x| + C

Question 12

sec x dx

Answer 12

ln |sec x + tan x| + C

Question 13

csc x dx

Answer 13

-ln |csc x + cot x| + C

Question 14

dx

square rot of a^2-x^2

Answer 14

arcsin x/a +c

Question 15

dx/a^2+x^2

Answer 15

1/a arctan x/a +c

Question 16

dx

x square root of x^2-a^2

Answer 16

1/a arcsec x/a +c

Question 17

Law of exponential growth and decay

Answer 17

y = Ce^kt

Question 18

FTC

Answer 18

integral from a to b of f(x) dx = F(b) - F(a)

Question 19

Average value of an integral or a funciton on an interval

Answer 19

1/b-a integral

Question 20

num>denom

Answer 20

infinity

Question 21

num<denom>
</denom>

Answer 21

o

Question 22

reiman sum

Answer 22

b-a

n

Question 23

trapezoid sum

Answer 23

b-a

2n

inside points counted twice

Question 24

area

Answer 24

top-bottom integral

Question 25

volume

Answer 25

pi integral R^2

or pi integral R^2-r^2

or integral area of base

or integral (side)^2

Question 26

area of a trapezoid

Answer 26

b1+b2 *h

2