Integration 2 - [Pure 3].

Question 1

What is Integration?

Answer 1

The reverse of Differentiation.

Question 2

What is the difference between a definite and indefinite integral?

Answer 2

A definite integral has bounds which are given. An indefinite integral has no limits and has a +c term.

Question 3

How do you solve ∫uⁿ du?

Answer 3

∫uⁿ du = 1/(n+1) uⁿ⁺¹ + c.

Question 4

How do you solve ∫e^u du?

Answer 4

∫e^u = e^u + c.

Question 5

How do you solve ∫1/u du?

Answer 5

∫1/u du = ln u + c.

Question 6

How do you solve ∫cos u du?

Answer 6

∫cos u du = sin u + c.

Question 7

How do you solve ∫sin u du?

Answer 7

∫sin u du = - cos u + c.

Question 8

How do you integrate a fraction using ln?

Answer 8

∫f’(x)/ f(x) dx = ln|f(x)| + c.

Question 9

What different types of Integration are there?

Answer 9

• Integration by Substitution.
• Integration by Parts.

Question 10

How do you integrate by substitution?

Answer 10

1. Differentiate the equation given to make dx the subject.
2. Change the limits if appropriate.
3. Sub in all the things you know.

Question 11

What formula from the formulae booklet are you given for Integration by Parts?

Answer 11

∫(u)(dv/dx) dx = uv - ∫(v)(du/dx) dx.

Question 12

What acronym do you use to work out what to choose for ‘u’ in Integration by Parts?

Answer 12

LATE Acronym.
* Ln.
* Algebra.
* Trigonometry.
* Exponentials.