Definite integrals of odd functions

​definite integrals of odd functions

11.11.2022​

1. Form groups of 4.

2. Scan the QR codes using 2 devices.

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​Some text here about the topic of discussion.

​instructions

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​Via: Quizizz

​Lesson flow:

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​wifi problem

​Losers are usually the ones who do not complete the pre-lesson worksheet.

Multiple Choice

Q1

Warm up: Click on button 2 and 3.

Does $$y=g\left(-x\right)$$  and $$y=-g\left(x\right)$$  represent the same graph?

• Yes

• No

Fill in the Blanks

Q2

Warm up: to test the function

Odd one out - give your option WITH EXPLANATION.

A. $y=\cos\ \left(\frac{x}{2}\right)$  

B. $y=x^3\cos\left(\frac{x}{2}\right)\sqrt{4-x^2}$  

C. $y=2^x$  

D. $y=\frac{1215}{x+2022}$  

Fill in the Blanks

Q3

Warm up: Click on button 5.

Drag $\alpha$  slowly from $0\degree$  to $180\degree$  .

Fill in the blanks.

The graph of $y=g\left(x\right)$  has (fill in this blank) symmetry about the origin.

Fill in the Blanks

Q4

Click on button 6 and 7.

Comment on the relationship between area A and B.

Fill in the Blanks

Q5

Denote $\int_0^2\ g\left(x\right)\ dx$  by $B$  . Express $\int_{-2}^0\ g\left(x\right)dx$  in terms of $B$  .

Multiple Choice

Q6

Does the equality $$\int_{-2}^2\ g\left(x\right)\ dx=\int_{-2}^0\ g\left(x\right)\ dx+\int_0^2\ g\left(x\right)\ dx$$  hold?

• Yes

• No

Fill in the Blanks

Q7

Hence, or otherwise, write down the value of $\int_{-2}^2\ g\left(x\right)\ dx$  .

This is veli useful arr!

​wifi problem

​Losers are usually the ones who do not complete the pre-lesson worksheet.

Multiple Choice

Q8

Does the following equality holds?

$$\int_{-2}^2\left(x^3\cos\left(\frac{x}{2}\right)+\frac{1}{2}\right)\sqrt{4-x^2}\ dx=\int_{-2}^2g\left(x\right)\ dx+\frac{1}{2}\int_{-2}^2\ \sqrt{4-x^2}\ dx$$  

• Yes

• No

Fill in the Blanks

Q9

Write down the value of $\int_{-2}^2\ \left(x^3\cos\left(\frac{x}{2}\right)+\frac{1}{2}\right)\sqrt{4-x^{2\ }}\ dx$  .

Round off your answer to 10 significant figures.

​ First come first serve - 5 Bonus points for the group!

​what do we learn today?