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Mathematik-Online problems:

Problem 123: Area under a Curve


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

For each $ a>0$ let $ f_a: D_a\longrightarrow\mathbb{R}$ be defined by

$\displaystyle f_a(x)=\frac{\sqrt{a^2-x^2}}{a^2}, \qquad {\mbox{for all}} \ x\in D_a. $

a)
Find the domain $ D_a\subset\mathbb{R}$ of $ f_a$ and test the function for roots and lokal extremums. Sketch the graph of $ f_3$ .
b)
Find the area between the graph of $ f_3$ and the $ x$ -axis.

Hint: Substitute $ x=a\sin u$ .

(Authors: Apprich/Höfert)

see also:


[Solutions]

  automatisch erstellt am 16. 11. 2007