Integration Apps

Question 1

Basic substitution is a lot like what rule of differentiation?

Answer 1

The chain rule.

Question 2

What’s the difference between implicit differentiation and differentials?

Answer 2

no derivative is 1, use d instead of ′

Question 3

List the 6 steps of basic substitution.

Answer 3

1) pick u
2) find differential
3) Build du
4) Substitute
5) Integrate
6) Replace u’s with x’s

Question 4

Even if a problem doesn’t look like a standard substitution, it’s often used if you can find what two things?

Answer 4

Something and its derivative

Question 5

If you integrate two ways and get two different answers, what do you know about the two?

Answer 5

They differ by a constant.

Question 6

n a vertical rectangle slice what’s the width?

Answer 6

dx

Question 7

In a horizontal rectangle slice, what’s the height?

Answer 7

dy

Question 8

How do you know in an area problem what variable to
use to form the bounds of the integration?

Answer 8

By the “d” variable

Question 9

How do you know when slicing area to use dx or dy?

Answer 9

If the thin side is a small change in x or y