Derivative and Integrals for Trig functions

Question 1

d/dx sin𝑥

Answer 1

cosx

Question 2

d/dx cosx

Answer 2

-sinx

Question 3

d/dx tanx

Answer 3

sec^2x

Question 4

d/dx csc x

Answer 4

-csc x * cot x

Question 5

d/dx sec x

Answer 5

sec x * tan x

Question 6

d/dx cot x

Answer 6

-csc^2 x

Question 7

integral sin x dx

Answer 7

• cos x + C

Question 8

integral cos x dx

Answer 8

sin x + C

Question 9

integral tan x dx

Answer 9

-ln |cos x | + C

Question 10

integral cot x dx

Answer 10

ln|sin x | + C

Question 11

integral sec x dx

Answer 11

ln | sec x + tan x | + C

Question 12

integral csc x dx

Answer 12

ln |csc x - cot x| + C

Question 13

d/dx arcsin x

Answer 13

1 / (1-x^2)^0.5

Question 14

d/dx arctan x

Answer 14

1 / (1 + x^2)

Question 15

d / dx arcsec x

Answer 15

1 / [ |x| (x^2 -1)^0.5]

Question 16

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

Answer 16

arcsin (x/a) + C

Question 17

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

Answer 17

1/a arctan(x/a) + C

Question 18

integral 1 / [x(x^2 - a^2)^0.5]

Answer 18

1 / a arcsec( |x| / a ) + C