Integral rules

Question 1

∫au^ndx =

Answer 1

(au^n+1)/n+1 + c

Question 2

∫(c+u)dx =

c = constant

Answer 2

∫(c)dx + ∫(u)dx + c

Question 3

∫(c)dx =

c = constant

Answer 3

cx + c

Question 4

∫(cu)dx =

Answer 4

c∫(u)dx

Question 5

∫(sin(x))dx =

Answer 5

-cos(x) + c

Question 6

∫(cos(x))dx =

Answer 6

sin(x) + c

Question 7

∫(sec^2(x))dx =

Answer 7

tan(x) +c

Question 8

∫(csc^2(x)dx =

Answer 8

-cot(x) + c

Question 9

∫(sec(x) ⋅ tan(x))dx =

Answer 9

sec(x) + c

Question 10

∫(csc(x) ⋅ cot(x))dx =

Answer 10

-csc(x) + c

Question 11

∫(e^n)dx =

Answer 11

e^n

Question 12

∫(1/x)dx =

Answer 12

ln|x|

Question 13

What is the fundamental theorem of calculus (FTC)?

Answer 13

(^a)(_b)∫f(x)dx = F(b) - F(a)

Question 14

d/dx[∫f(x)dx] =

Answer 14

f(x)

Question 15

What is sigma notation?

Answer 15

Lim(n->∞) Σf(xi)Δx

Question 16

How do you find Δx for sigma notation?

Answer 16

(b-a)/n

Question 17

How do you find xi for sigma notation?

Answer 17

a + kΔx

Question 18

What is another way to find a trapezoid sum besides doing the entire area calculation?

Answer 18

(RRAM + LRAM)/2

Question 19

∫sinh(x)dx =

Answer 19

cosh(x) + c

Question 20

∫cosh(x)dx =

Answer 20

sinh(x) + c

Question 21

∫tanh(x)dx =

Answer 21

ln|cosh(x)| + c

Question 22

∫sech(x)dx =

Answer 22

tan^-1(sinh(x)) + c

Question 23

∫coth(x)dx =

Answer 23

ln|sinh(x)| + c

Question 24

∫csch(x)dx =

Answer 24

ln|tanh(x/2)| + c