Processing Math: Done
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
No jsMath TeX fonts found -- using image fonts instead.
These may be slow and might not print well.
Use the jsMath control panel to get additional information.
jsMath Control PanelHide this Message

jsMath

Lösung 2.2:3a

Aus Online Mathematik Brückenkurs 2

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
K (Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel))
K (Solution 2.2:3a moved to Lösung 2.2:3a: Robot: moved page)

Version vom 10:22, 11. Mär. 2009

The secret behind a successful substitution is to be able to recognize the integral as an expression of the type

an expressionin uudx 

where u=u(x) is the actual substitution. In the integral

2xsinx2dx 

we see that the expression x2 is the argument for the sine function, as the same time as its derivative x2=2x  stands as a factor in front of sine. Therefore, if we set u=x2, the integral, the integral will be of the form

usinudx. 

Thus, we can use u=x2 for the substitution,

2xsinx2dx=udu=x2=2xdx=sinudu=−cosu+C=−cosx2+C. 
Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_2.2:3a“