Kap 5 integrasjon

Question 1

Hva definerer en jevn funksjon

Answer 1

f(-x)=f(x)

Question 2

Hva definerer en odde funksjon

Answer 2

g(-x)=-g(x)

Question 3

int 1

Answer 3

x

Question 4

int x

Answer 4

(1/2)*x^2

Question 5

int x^2

Answer 5

(1/3)*x^3

Question 6

int 1/x^2

Answer 6

-(1/x)

Question 7

int 1/x

Answer 7

ln(abs(x))

Question 8

int sqrt(x)

Answer 8

(2/3)*x^(3/2)

Question 9

int 1/(sqrt(x))

Answer 9

2*sqrt(x)

Question 10

int sin ax

Answer 10

-(1/a)*cos ax

Question 11

int cos ax

Answer 11

(1/a)*sin ax

Question 12

int sec^2(ax)

Answer 12

(1/a)*tan ax

Question 13

int csc^2(ax)

Answer 13

(1/a)*sin ax

Question 14

int sec ax tan ax

Answer 14

(1/a)sec ax

Question 15

int csc ax cot ax

Answer 15

-(1/a)csc ax

Question 16

int 1/ sqrt(a^2 -x^2)

Answer 16

arcsin (x/a)

Question 17

int 1/(a^2+x^2)

Answer 17

(1/a)arctan (x/a)

Question 18

int e^(ax)

Answer 18

1/a)*e^(ax)

Question 19

int b^(ax)

Answer 19

1/(alnb))*b^(ax)

Question 20

int cosh ax

Answer 20

1/a)sinh ax

Question 21

int sinh ax

Answer 21

1/a)cosh ax

Question 22

int tan x

Answer 22

ln(abs(sec x))

Question 23

int cot x

Answer 23

ln(abs(sin x))

Question 24

int sec x

Answer 24

ln(abs(sec x +tan x))

Question 25

int csc x

Answer 25

-ln(abs(csc x+cot x))

Question 26

int cos^2(x)

Answer 26

1/2(x+sinx*cosx)

Question 27

int sin^2(x)

Answer 27

1/2(x-sinx*cosx)