Chapter 23 - Trigonometry in Integration

Question 1

What is the integration of sin x ?

Answer 1

• cos x + c

Question 2

What is the integration of -sin x ?

Answer 2

cos x + c

Question 3

What is the integration of sin(func) ? where func can be any function involving x

Answer 3

• 1/ dydx (func) cos (func) + c`

Question 4

Talk about the process of integration sin(ax+b) or in previous example sin(func)?

Answer 4

Differentiate func. Change sin into - cos. Divide number before -cos by derivative. The number after -cos is the same as number after sin prior to integration.

Question 5

What is the integration of cos(func)?

Answer 5

1/ dydx(func) sin(func) + c

Question 6

Talk about the process of integration of cos(ax+b) or cos(func in previous example).

Answer 6

Differentiate func. Change cos into sin. Divide number before sin by derivative. The number after sin is the same as number after cos initially.

Question 7

What is the integration of cos x ?

Answer 7

sinx + c

Question 8

What is the integration of -cosx?

Answer 8

-sinx + C

Question 9

What is the integration of sec^2 x ? (this is in the formula book!)

Answer 9

tan x + c

Question 10

What is the integration of sec^2 (func of x)?

Answer 10

1/ dydx (func) tan (func) + c

Question 11

What is the integration of cosecxcotx? (this is in the formula book)

Answer 11

• cosec x + c

Question 12

What is the integration of cosec(func)cot(func)?

Answer 12

• 1/ dydx (func) cosec (func) + c

Question 13

What is the integration of - cosecxcotx? (this is in the formula book)?

Answer 13

cosec x + c

Question 14

What is the integration of secxtanx? (this is in the formula book)

Answer 14

sec x + c

Question 15

What is the integration of sec(func)tan(func)?

Answer 15

1/ dydx (func) sec (func) + c

Question 16

What is the integration of - secxtanx? (this is in the formula book)

Answer 16

• sec x + c

Question 17

What is the integration of - sec (func) tan (func) ?

Answer 17

• 1/ dydx (func) sec(func) + c

Question 18

What is the integration of cosec^2 x? (this is in your formula book)

Answer 18

• cot x + c

Question 19

What is the integration of -cosec^2 x ? (this is in your formula book)

Answer 19

cot x + c

Question 20

What is the integration of cosec^2 (func)?

Answer 20

• 1 / dydx (func) cot(func) + c

Question 21

What is the integration of -cosec^2(func)?

Answer 21

1/ dydx (func) cot (func) + c

Question 22

If we have to integrate tan x what can we change it into prior to integration?

Answer 22

sinx/cosx

Question 23

What would this be after integration?

Answer 23

-ln cos x + c

Question 24

if we have to integrate cot x, what can we do prior?

Answer 24

cos x / sinx

Question 25

What would this be after integration

Answer 25

ln sinx + c

Question 26

Integrate tanx

Answer 26

ln sec x + c

Question 27

Integrate tankx. Explain what happened here

Answer 27

1/k sec x + c We differentiate the value inside tanx and divided the integrate tan (ln seckx)by it. Remember the function inside sec will stay the same as the one inside tan initially.

Question 28

What is the integration of cosec x?

Answer 28

-ln cosec x + cos x + c

Question 29

What is the integration of sec x ?

Answer 29

ln sec x + tan x + c

Question 30

What is the integration of cot x?

Answer 30

ln sinx + c