Calc II

Question 1

integrate:

xⁿ dx

Answer 1

xⁿ⁺¹
n+1

Question 2

integrate:

k dx

Answer 2

kx + C

Question 3

integrate:

e^x dx

Answer 3

e^x + C

Question 4

integrate:

a^x dx

Answer 4

a^x +C
ln|a|

Question 5

integrate:

1
x

Answer 5

ln|x|+C

Question 6

integrate:

sin(x) dx

Answer 6

-cos(x) + C

Question 7

integrate:

cos(x) dx

Answer 7

sin(x) + C

Question 8

integrate:

sec²(x) dx

Answer 8

tan(x) + C

Question 9

integrate:

csc²(x) dx

Answer 9

-cot(x) + C

Question 10

integrate:

sec(x)tan(x) dx

Answer 10

sec(x) + C

Question 11

integrate:

csc(x)cot(x) dx

Answer 11

-csc(x) + C

Question 12

integrate:

______1______
√ ￣1-x²￣

Answer 12

sin^-1(x) + C

Question 13

integrate:

1
x²-1

Answer 13

tan^-1(x) + C

Question 14

integrate:

tan(x) dx

Answer 14

ln|sec(x)| + C

Question 15

integrate:

sec(x) dx

Answer 15

ln|sec(x) + tan(x)| + C

Question 16

integrate:

1
x²+a²

Answer 16

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

Question 17

trig identities:

sin²(x)+cos²(x)

Answer 17

= 1

Question 18

trig identities:

tan²(x) + 1

Answer 18

sec²(x)

Question 19

trig identities:

1 + cot²(x)

Answer 19

csc²(x)

Question 20

trig identities:

cos²(x)

Answer 20

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

Question 21

trig identities:

sin²(x)

Answer 21

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

Question 22

trig identities:

sin(2x)

Answer 22

2 sin(x)cos(x)

Question 23

trig identities:

cos(2x)

Answer 23

cos²(x) - sin²(x)

Question 24

substitute:

______
√ a² - x²

Answer 24

x = a sin(θ)

Question 25

# substitute: ______ √ x² - a²

Answer 25

x = a sec(θ)

Question 26

# substitute: ______ √ x² + a²

Answer 26

x = a tan(θ)

Question 27

# formula: Area under a Polar Curve

Answer 27

∫ 1/2 πr²

Question 28

# formula: Integration By Parts (∫ udv)

Answer 28

∫udv = uv - ∫vdu

Question 29

# formula: washer method .

Answer 29

pi ∫R^2 - r^2 .

Question 30

shell method .

Answer 30

2pi ∫ rh dx .

Question 31

# series tests: if lim an =/= 0 .

Answer 31

an = divergent nth term test

Question 32

if lim an = 0 .

Answer 32

INCONCLUSIVE .

Question 33

if ∫an = definite ..

Answer 33

series is convergent integral test

Question 34

# uh if ∫an = indefinite ..

Answer 34

series is divergent integral test

Question 35

sum _1_ n^p p <= 1

Answer 35

divergent p-series .

Question 36

∑ _1_ n^p p > 1

Answer 36

convergent p-series.

Question 37

sum of a geometric series

Answer 37

_first term_ ( 1 - ratio)