5.5 Substitution

Question 1

Substitution is to Integration as __________ is to Differentiation

Answer 1

Chain Rule

Question 2

Steps of Integrating using Substitution

Answer 2

1) Find u such that u du is similar to x dx
2) substitute u and du– there should no longer be any terms of x
3) integrate in terms of u
4) replace u with the x term

Question 4

Revaluating limits of Definite Integral using Substitution

Answer 4

Take the function u at the upper and lower bounds and replace

Integral of x dx from a to b

Becomes

Integral of u du from u(a) to u(b)

FTOC: Integral of u du at u(b) - Integral of u du at u(a)

Question 5

Step 6 of Integrating using Substitution

Answer 5

Replace u with the original equation you picked in terms of x

Question 6

Average of a function

Answer 6

Integrate function, divide by domain