Antiderivative Rules and Methods

Question 1

What do we call F(x) such that dF/dx = f(x)?

Answer 1

Antiderivative

Question 2

Power Rule: ∫x^n dx = ?

Answer 2

[x^(n + 1)]/(n + 1) + C

Question 3

When does the Power Rule not work?

Answer 3

When the exponent is -1

Question 4

Constant Multiple Rule:
∫a*f(x) dx = ?

Answer 4

a∫f(x) dx

Question 5

Sum/Difference Rule:
∫f(x) + g(x) dx = ?

Answer 5

∫f(x) dx + ∫g(x) dx

Question 6

Can you use a product or quotient rule for integrals?

Answer 6

No

Question 7

For constant a:
∫a dx = ?

Answer 7

ax + C

Question 8

∫e^x dx = ?

Answer 8

e^x + C

Question 9

∫1/x dx = ?

Answer 9

ln|x| + C

Question 10

∫cos(x) dx = ?

Answer 10

sin(x) + C

Question 11

∫sin(x) dx = ?

Answer 11

-cos(x) + C

Question 12

∫x^-1 dx = ?

Answer 12

∫1/x dx = ln|x| + C

Question 13

Which method of evaluating antiderivatives undoes the chain rule?

Answer 13

U-substitution

Question 14

Formula for integrating by parts

Answer 14

∫u dv = uv - ∫v du

Question 15

When integrating by parts, what is the requirement for assigning one part as dv?

Answer 15

It must be something you can integrate

Question 16

When integrating by parts, what is the requirement for assigning one part as u?

Answer 16

It must get nicer when you take the derivative

Question 17

What two things are required for u-substitution?

Answer 17

The function u and its derivative behind the integrand ∫

Question 18

For ∫(linear)f(linear), what method do you use?

Answer 18

Parts, then u-sub