## 12 HL: Definite Integrals.

Complete as many of the following questions as you can before our next class (we’ll continue to work on these in our next class as well).

Exercise 22A questions 3–8, 12 (just complete the centre column for 3–8 and 12), 14, 16, 21

## 12 HL: Trigonometric Substitutions

In class we arrived at part of the solution to $$\int \sqrt{2-x^2}\;d x$$, using the substitution $$x = \sqrt{2}\sin \theta$$. Complete this question by showing that $\int \sqrt{2-x^2}\;d x=\left( \frac{x}{\sqrt{2}} \right) \sqrt{ 1-\frac{x^2}{2}} +\arcsin \left(\frac{x}{\sqrt{2}}\right) + C$

Hint
Note that, given our substitution choice, it follows that $$\sin \theta = \frac{x}{\sqrt{2}}$$. Can we do something similar for $$\cos \theta$$?

Also complete

Exercise 21E questions 4, 5d, 6
Exercise 21F questions 12ad, 17, 18bd

## 11 SL: Absolute Value Functions

Complete the following questions before our next class.

Exercise 3G questions 2–4
Review Set 3A questions 2, 3, 6, 10a, 12, 19

## 12 HL: Integration by Substitution

Complete the following questions before our next class.

Exercise 21F questions 3, 4bce, 5bf, 8dh, 9ae

## 12 HL: Integration by Parts

Complete the following questions before our next class.

Exercise 21G questions 1, 3, 4ab, 6ac
Exercise 21D questions 12, 15, 19, 20

## 11 SL: The Absolute Value Function

Complete the following questions before our next class.

Exercise 3F questions 1 and 3
Exercise 3G question 1

## 11 SL: Inverse Functions

Complete the following questions before our next class.

Exercise 3F questions 2, 4–12, 14

## 11 Math SL: Composite Functions

Complete the following questions before our next class.

Exercise 3E questions 2, 4, 6, 7, 9, 10, 11,12

## 12 HL: Rules for Integration

Complete the following questions before our next class.

Exercise 21B questions 1acgh, 2ac, 3def, 4dg, 7ae, 8aef, 9, 12a, 14
Exercise 21C questions 1ac, 2, 6, 7b

## 12 HL: Indefinite Integrals

Complete the following questions before our next class.

Exercise 20C questions 1, 2ai, ii, b, 3ai, ii, b, 4abc
Exercise 21A questions 2abd, 3c, 9