abMathematics

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 \[\int \sqrt{2-x^2}\;d x=\left( \frac{x}{\sqrt{2}} \right) \sqrt{ 1-\frac{x^2}{2}} +\arcsin \left(\frac{x}{\sqrt{2}}\right) + C\]

Also complete

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

Complete the following questions before our next class.

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

Complete the following questions before our next class.

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

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