KTH.SE:u1zpa8nw den 18 juli 2007 kl. 08.37

KTH.SE:u1zpa8nw — Wed, 18 Jul 2007 08:37:42 GMT

KTH.SE:u1zpa8nw: Ny sida: '''Övning 2.2:1'''
Beräkna integralerna

KTH.SE:u1zpa8nw — Wed, 18 Jul 2007 08:36:39 GMT

Ny sida: '''Övning 2.2:1''' <div class="ovning" style="margin-top:-20px; margin-bottom:-18px;"> Beräkna integralerna <table width="100%" cellspacing="10px"> <tr align="left" valign="top"> <td clas...

Ny sida
'''Övning 2.2:1'''
<div class="ovning" style="margin-top:-20px; margin-bottom:-18px;">
Beräkna integralerna
<table width="100%" cellspacing="10px">
<tr align="left" valign="top">
<td class="ntext">a)</td>
<td class="ntext" width="100%">$\displaystyle \int_{1}^{2} \displaystyle\frac{dx}{(3x-1)^4}$ genom att använda substitution $u=3x-1$</td>
</tr>
<tr align="left" valign="top">
<td class="ntext">b)</td>
<td class="ntext" width="100%">$\displaystyle \int (x^2+3)^5x \, dx$ genom att använda substitution $u=x^2+3$</td>
</tr>
<tr align="left" valign="top">
<td class="ntext">c)</td>
<td class="ntext" width="100%">$\displaystyle \int x^2 e^{x^3} \, dx$ genom att använda substitution $u=x^3$</td>
</tr>
<tr><td height="5px"/></tr>
</table>
</div>

'''Övning 2.2:2'''
<div class="ovning" style="margin-top:-20px; margin-bottom:-18px;">Beräkna integralerna
<table width="100%" cellspacing="10px">
<tr align="left">
<td class="ntext">a)</td>
<td class="ntext" width="50%">$\displaystyle\int_{0}^{\pi} \cos 5x\, dx$</td>
<td class="ntext">b)</td>
<td class="ntext" width="50%">$\displaystyle\int_{0}^{1/2} e^{2x+3}\, dx$</td>
</tr>
<tr align="left">
<td class="ntext">c)</td>
<td class="ntext" width="50%">$ \displaystyle\int_{0}^{5} \sqrt{3x + 1} \, dx$</td>
<td class="ntext">d)</td>
<td class="ntext" width="50%">$\displaystyle\int_{0}^{1} \sqrt[\scriptstyle3]{1 - x}\, dx$</td>
</tr>
</table>
</div>

'''Övning 2.2:3'''
<div class="ovning" style="margin-top:-20px; margin-bottom:-18px;">Beräkna integralerna
<table width="100%" cellspacing="10px">
<tr align="left">
<td class="ntext">a)</td>
<td class="ntext" width="50%">$\displaystyle\int 2x \sin x^2\, dx$</td>
<td class="ntext">b)</td>
<td class="ntext" width="50%">$\displaystyle\int \sin x \cos x\, dx$</td>
</tr>
<tr align="left">
<td class="ntext">c)</td>
<td class="ntext" width="50%">$ \displaystyle\int \displaystyle\frac{\ln x}{x}\, dx$</td>
<td class="ntext">d)</td>
<td class="ntext" width="50%">$\displaystyle\int \displaystyle\frac{x+1}{x^2+2x+2}\, dx$</td>
</tr>
<tr align="left">
<td class="ntext">e)</td>
<td class="ntext" width="50%">$ \displaystyle\int \displaystyle\frac{3x}{x^2+1}\, dx$</td>
<td class="ntext">f)</td>
<td class="ntext" width="50%">$\displaystyle\int \displaystyle\frac{\sin \sqrt{x}}{\sqrt{x}}\, dx$</td>
</tr>
</table>
</div>

'''Övning 2.2:4'''
<div class="ovning" style="margin-top:-20px; margin-bottom:-18px;">Använd formeln $$\int \frac{dx}{x^2+1} = \arctan x + C$$ för att beräkna integralerna
<table width="100%" cellspacing="10px">
<tr align="left">
<td class="ntext">a)</td>
<td class="ntext" width="50%">$\displaystyle\int \frac{dx}{x^2+4}$</td>
<td class="ntext">b)</td>
<td class="ntext" width="50%">$\displaystyle\int \frac{dx}{(x-1)^2+3}$</td>
</tr>
<tr align="left">
<td class="ntext">c)</td>
<td class="ntext" width="50%">$ \displaystyle\int \frac{dx}{x^2+4x+8}$</td>
<td class="ntext">d)</td>
<td class="ntext" width="50%">$\displaystyle\int \frac{x^2}{x^2 +1}\, dx$</td>
</tr>
</table>
</div>