Exam 2

Question 1

∫x^n dx

Answer 1

1/n+1 X^n+1 +C

Question 2

∫1/x dx

Answer 2

ln|x|+C

Question 3

∫1/(ax+b)dx

Answer 3

1/a ln|a+b|+C

Question 4

∫lnax dx

Answer 4

x(lnax -1)

Question 5

∫a^x dx

Answer 5

a^x /lna +C

Question 5

∫e^x dx

Answer 5

e^x +c

Question 6

∫cscxdx

Answer 6

ln|tanx/2|+C

Question 7

∫csc^2(ax)dx

Answer 7

-1/a cot(ax)+C

Question 8

∫sin(ax) dx

Answer 8

-1/a cos(ax)+C

Question 8

∫secx *cscx dx

Answer 8

ln|tanx|+C

Question 9

∫cos(ax)

Answer 9

1/asin(ax)+C

Question 10

∫tan(ax) dx

Answer 10

-1/a ln(cos(ax)) +C

Question 11

∫sec^2 (ax) dx

Answer 11

1/a tan(ax) +C

Question 12

∫sec(x)tan(x) dx

Answer 12

secx +C

Question 13

∫secx dx

Answer 13

ln|secx+tanx|+C

Question 14

work

Answer 14

(a to b)∫ F(x) dx

Question 15

Force of spring

Answer 15

spring constant * distance stretched

Question 16

Force of y

Answer 16

mass *gravity

Question 17

what is density * volume

Answer 17

mass

Question 18

∫lnx dx

Answer 18

x(lnx-1)+C

Question 19

∫du / sqrt(a^2 - u^2)

Answer 19

sin^-1 (u/a)+C

Question 19

∫log(base a)x

Answer 19

x/lna (lnx-1)+C

Question 20

∫du/ a^2 +u^2

Answer 20

1/a tan^-1 (u/a)+C

Question 21

work for water

Answer 21

(a to b) ∫densitygravityarea*x

Question 22

∫du/ u(sqrt(u^2 -a^2)

Answer 22

1/a sec^-1(u/a) +C

Question 23

∫udv

Answer 23

uv -∫ vdu +C

Question 24

LIATE

Answer 24

Log , inverse trig, alegriaic, trig, exponential

Question 25

integrating sin+cos products with odd power trig

Answer 25

1. write odd as even power * 1 of it
   2.get it in terms of the other
2. integrate making u the higher power

Question 26

integrating sin+cos products with both even powers

Answer 26

1. double angle identities to get into polynomial of cos(2x)
2. apply strategies to things with powers greater than 1

Question 27

double angle cos^2(x)

Answer 27

1/2 (1+cos(2x)

Question 28

double angle for sin^2(x)

Answer 28

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

Question 29

identity for cos^2(x)

Answer 29

1-sin^2(x)

Question 29

identity for sin^2(x)

Answer 29

1-cos^2(x)

Question 30

sin(ax)cos(bx)

Answer 30

1/2 sin((a+b)x +1/2 sin ((a-b)x)

Question 31

cos(ax)cos(bx)

Answer 31

1/2 cos((a+b)x +1/2 cos ((a-b)x)

Question 32

tan is even sec is odd

Answer 32

1. write tan in terms of secx
2. write polynomial in sec
   3 reduction method

Question 32

integrating tan+sec products with sec being even

Answer 32

1.split out a sec^2(x) while keeping secx to even power
2.u sub with tan as u

Question 33

integrating sin+cos products with odd power tan

Answer 33

1. split out secxtanx
   2 write tan in even power
2. u is secx

Question 34

identity of sec^2(x)

Answer 34

tan^2(x) +1

Question 35

tan reduction formula
tan^n (x) dx

Answer 35

1/n-1 tan^(n-1) (x) - ∫tan^ (n-2) (x)dx

Question 36

sec reduction formula
sec^n (x) dx

Answer 36

1/n-1 sec^(n-2) (x)tan(x) + n-2/(n-1)
∫tan^ (n-2) (x)dx

Question 37

trig sub a^2-x^2

Answer 37

x = asin(theta)

Question 38

trig sub a^2 + x^2

Answer 38

x = atan(theta)

Question 39

trig sub x^2 - a^2

Answer 39

x = a(sec(theta)