Trigonometric Integrals 6.3

Question 1

what do we transform the integral of products of sin+cos and tan+sec

Answer 1

a u and du

Question 2

when you have odd cosines, your u should be

Answer 2

sinx

Question 3

when you have odd sines your u should be..

Answer 3

cos

Question 4

when you have odd tangents, your u should be..

Answer 4

sec

Question 5

When you have odd secants, your u should be..

Answer 5

tanx

Question 6

you should keep splitting/converting until you…

Answer 6

have the u’s derivative by itself

Question 7

sinx squared plus cos sqaured =

Answer 7

1

Question 8

tanx squared + 1 =

Answer 8

secx sqaured

Question 9

sinx squared =

Answer 9

1- cos2x /2

Question 10

cos sqaured

Answer 10

1+ cos2x /2

Question 11

How to solve odd sin

Answer 11

take a sin out, and convert the rest to cosine using trig identity that gives you sin^2 = 1 - cos^2
then usub

Question 12

How to solve odd cos

Answer 12

take a cos out, and convert the rest to sin by trig identity cos^2 = 1 - sin^2 then u sub

Question 13

How to solve a even sin and even cos

Answer 13

use fraction identities and
keep a squared inside when taking an exponent out
convert inside sine and cosine to fraction identites

Question 14

When both sin and cos are odd, how you expand and what to use for u

Answer 14

expand the smaller one and your u is the larger exponent

Question 15

what to separate with odd tangents

Answer 15

take out a tan and convert the rest to sec

Question 16

What to separate with even secant

Answer 16

take out a secx squared and convert the rest to tan

Question 17

What to separate with even tan

Answer 17

get a tanx squared to convert to sec

Question 18

When youare multiplying sins and coss and your angle is not a single variable…

Answer 18

use it as a u

Question 19

how to solve a odd tan and odd sec

Answer 19

get a squared of any and convert to the other type

Question 20

to use the identities sin^2 = 1 - cos2x / 2 and cos^2 = 1 - cos2x + 1, you need… and how to fix it

Answer 20

you need a single variable without a constant as angle

to fix, use u sub then solve as you would

Question 21

if you have a ax^2 +bx + c, what do you do?

Answer 21

complete the square