The Anti-Derivative

Question 1

If f(x) has derivative 0…

Answer 1

f(x) is a constant function

Question 2

If f’(x) = g’(x)…

Answer 2

they differ by a constant

Question 3

Primative/anti-derivative

Answer 3

When the derivative of F(x) is f(x)

Question 4

general primative of f(x)

Answer 4

F(x) + C

Question 5

If y’= X^n, y=…

Answer 5

y= x^n+1/n+1 + C

add 1 to power, divide by new power

Question 6

If y’= (ax+b)^n, y=…

Answer 6

y= (ax+b)^n+1/a(n+1) +C

Add 1 to power, divide by new power X by derivative of (ax+b)

Question 7

how to find function given derivative and initial condition

Answer 7

find the anti-derivative

sub known values to calculate the constant C

Question 8

how to use reverse chain rule

Answer 8

put intergral in form of f'(x) x f(x)^n
then f(x)^n+1/n+1

Question 9

primitive of:
cosx
cos(ax+b)

Answer 9

sinx

1/a sin(ax+b)

Question 10

primitive of:
sinx
sin(ax+b)

Answer 10

• cosx

- 1/a cos(ax+b)

Question 11

primitive of:
sec^2x
sec^(ax+b)

Answer 11

tanx

1/a tan(ax+b)

Question 12

primitive of e^(ax + b)

Answer 12

1/a e^(ax + b)

1/a times by original function

Question 13

primitive of a^f(x)

Answer 13

a^f(x)/lna x f’(x)

original function divided by ln(base) x derivative of power

Question 14

primitive of 1/x

Answer 14

ln/x/ + c

Question 15

primitive of f’(x) / f(x)

Answer 15

ln/f(x)/ + c