integrals

Question 1

x^n

Answer 1

(x^n+1)/(n+1) + C

Question 2

1/x

Answer 2

ln|x| + C

Question 3

u’/u

Answer 3

ln|u| + C

Question 4

e^x

Answer 4

e^x + C

Question 5

a^x

Answer 5

a^x/lna + C

Question 6

cosx

Answer 6

sinx + C

Question 7

sinx

Answer 7

-cosx + C

Question 8

sec^2 x

Answer 8

tanx + C

Question 9

tanx

Answer 9

-ln|cosx| + C

Question 10

u’/(a^2+u^2)

Answer 10

(1/a)arctan(u/a) + C

Question 11

u’/(a^2-u^2)^1/2

Answer 11

arcsin(u/a) + C

Question 12

cotx

Answer 12

ln|sinx| + C

Question 13

secxtanx

Answer 13

secx + C

Question 14

csc^2 x

Answer 14

-cotx + C

Question 15

cscxcotx

Answer 15

-cscx + C

Question 16

volume of a disc

Answer 16

V=pi%r^2

integral is b%a

Question 17

volume of a washer

Answer 17

V=pi%(R^2-r^2)

integral is b%a

Question 18

volume of a cross section

Answer 18

V=%A

integral is b%a

Question 19

fundamental theorem

Answer 19

%f’(x)dx=f(b) - f(a)

integral is b%a

Question 20

start plus accumulation

Answer 20

f(b)=f(a) + %f’(x)dx

integral is b%a

Question 21

second fundamental theorem

Answer 21

(d/dx)%f(t)dt=f(v)v’ - f(u)u’

integral is v%u

Question 22

area of trapezoid

Answer 22

A=(1/2)w(h1+h2)

Question 23

riemann sum

Answer 23

add areas of rectangles

Question 24

average value of a function

Answer 24

favg=(%f(x)dx)/(b-a) (avg height=area/width

integral is b%a

Question 25

displacement

Answer 25

%v(t)dt

integral is t2%t1

Question 26

total displacement

Answer 26

%|v(t)|dt

integral is t2/t1