class test jan'19

Question 1

(int) a

Answer 1

ax

Question 2

(int) x^b

Answer 2

x^b+1 / b+1

Question 3

(int) 1/x

Answer 3

ln|x|

Question 4

(int) sinx

Answer 4

-cosx

Question 5

(int) cosx

Answer 5

sinx

Question 6

(int) tanx

Answer 6

ln|secx|

Question 7

(int) secx

Answer 7

ln|secx + tanx|

Question 8

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

Answer 8

arcsin (x/a)

Question 9

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

Answer 9

1/a .arctan (x/a)

Question 10

(int) e^x

Answer 10

e^x

Question 11

(int) sinhx

Answer 11

coshx

Question 12

(int) coshx

Answer 12

sinhx

Question 13

what is integration by parts equation?

Answer 13

(int) u.v’
and so

u.v -(int) u’. v

Question 14

what makes a function even

Answer 14

if f(-x) = f(x)

Question 15

what makes a function odd

Answer 15

if f(-x)= -f(x)

Question 16

when do u do long division for functions

Answer 16

when its degree is higher on top (or equal to)

Question 17

double angle sin^2 x

Answer 17

1/2 (1-cos(2x))

Question 18

double angle cos^2 x

Answer 18

1/2 (1+cos(2x))

Question 19

sina.cosb

Answer 19

1/2[sin(a-b) +sin(a+b)]

Question 20

sina.sinb

Answer 20

1/2 [cos(a-b) -cos(a+b)]

Question 21

cosa.cosb

Answer 21

1/2 [cos(a-b) +cos(a+b)]

Question 22

rational function what is t, dx, cosx and sinx equal to

Answer 22

t=tan(x/2)

dx= 2/ (1+t^2) dt

cosx= (1-t^2) / (1+t^2)

sinx= 2t/ (1+t^2)

Question 23

sq root (bx+c)^2 + a^2

Answer 23

bx+c= a tanu

Question 24

sq root (bx+c)^2 - a^2

Answer 24

bx+c= a secu

Question 25

sq root a^2 - (bx+c)^2

Answer 25

bx+c= a sinu