Definite integrals of odd functions

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. $y=\frac{1215}{x+2022}$  

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.

Q4

Click on button 6 and 7.

Comment on the relationship between area A and B.

Q5

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

Q7

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

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.