Processing Math: 66%
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

2.1 Übungen

Aus Online Mathematik Brückenkurs 2

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
K
(Translated links into English)
Zeile 3: Zeile 3:
| style="border-bottom:1px solid #000" width="5px" |  
| style="border-bottom:1px solid #000" width="5px" |  
{{Ej vald flik|[[2.1 Inledning till integraler|Theory]]}}
{{Ej vald flik|[[2.1 Inledning till integraler|Theory]]}}
-
{{Vald flik|[[2.1 Exercises|Exercises]]}}
+
{{Vald flik|[[2.1 Övningar|Exercises]]}}
| style="border-bottom:1px solid #000" width="100%"|  
| style="border-bottom:1px solid #000" width="100%"|  
|}
|}
Zeile 22: Zeile 22:
|width="50%"| <math>\displaystyle\int_{-1}^{2}|x| \, dx</math>
|width="50%"| <math>\displaystyle\int_{-1}^{2}|x| \, dx</math>
|}
|}
-
</div>{{#NAVCONTENT:Svar|Svar 2.1:1|Lösning a|Lösning 2.1:1a|Lösning b|Lösning 2.1:1b|Lösning c|Lösning 2.1:1c|Lösning d|Lösning 2.1:1d}}
+
</div>{{#NAVCONTENT:Answer|Svar 2.1:1|Solution a|Lösning 2.1:1a|Solution b|Lösning 2.1:1b|Solution c|Lösning 2.1:1c|Solution d|Lösning 2.1:1d}}
===Exercise 2.1:2===
===Exercise 2.1:2===
Zeile 38: Zeile 38:
|width="50%"| <math>\displaystyle\int_{1}^{4} \displaystyle\frac{\sqrt{x}}{x^2}\, dx</math>
|width="50%"| <math>\displaystyle\int_{1}^{4} \displaystyle\frac{\sqrt{x}}{x^2}\, dx</math>
|}
|}
-
</div>{{#NAVCONTENT:Svar|Svar 2.1:2|Lösning a|Lösning 2.1:2a|Lösning b|Lösning 2.1:2b|Lösning c|Lösning 2.1:2c|Lösning d|Lösning 2.1:2d}}
+
</div>{{#NAVCONTENT:Answer|Svar 2.1:2|Solution a|Lösning 2.1:2a|Solution b|Lösning 2.1:2b|Solution c|Lösning 2.1:2c|Solution d|Lösning 2.1:2d}}
===Exercise 2.1:3===
===Exercise 2.1:3===
Zeile 54: Zeile 54:
|width="50%"| <math>\displaystyle\int \displaystyle\frac{x^2+1}{x}\, dx</math>
|width="50%"| <math>\displaystyle\int \displaystyle\frac{x^2+1}{x}\, dx</math>
|}
|}
-
</div>{{#NAVCONTENT:Svar|Svar 2.1:3|Lösning a|Lösning 2.1:3a|Lösning b|Lösning 2.1:3b|Lösning c|Lösning 2.1:3c|Lösning d|Lösning 2.1:3d}}
+
</div>{{#NAVCONTENT:Answer|Svar 2.1:3|Solution a|Lösning 2.1:3a|Solution b|Lösning 2.1:3b|Solution c|Lösning 2.1:3c|Solution d|Lösning 2.1:3d}}
===Exercise 2.1:4===
===Exercise 2.1:4===
Zeile 74: Zeile 74:
|width="100%"| Calculate the area of the region given by the inequality, <math>x^2\le y\le x+2</math>.
|width="100%"| Calculate the area of the region given by the inequality, <math>x^2\le y\le x+2</math>.
|}
|}
-
</div>{{#NAVCONTENT:Svar|Svar 2.1:4|Lösning a|Lösning 2.1:4a|Lösning b|Lösning 2.1:4b|Lösning c|Lösning 2.1:4c|Lösning d|Lösning 2.1:4d|Lösning e|Lösning 2.1:4e}}
+
</div>{{#NAVCONTENT:Answer|Svar 2.1:4|Solution a|Lösning 2.1:4a|Solution b|Lösning 2.1:4b|Solution c|Lösning 2.1:4c|Solution d|Lösning 2.1:4d|Solution e|Lösning 2.1:4e}}
===Exercise 2.1:5===
===Exercise 2.1:5===
Zeile 86: Zeile 86:
|width="100%"| <math>\displaystyle \int \sin^2 x\ dx\quad</math> (HINT: rewrite the integrand using a trigonometric formula)
|width="100%"| <math>\displaystyle \int \sin^2 x\ dx\quad</math> (HINT: rewrite the integrand using a trigonometric formula)
|}
|}
-
</div>{{#NAVCONTENT:Svar|Svar 2.1:5|Lösning a|Lösning 2.1:5a|Lösning b|Lösning 2.1:5b}}
+
</div>{{#NAVCONTENT:Answer|Svar 2.1:5|Solution a|Lösning 2.1:5a|Solution b|Lösning 2.1:5b}}

Version vom 08:55, 3. Sep. 2008

 
  1. REDIRECT Template:Nicht gewählter Tab
  2. REDIRECT Template:Gewählter Tab
 

Exercise 2.1:1

Interpret each integral as an area, and determine its value.

a) 2−12dx  b) 01(2x+1)dx 
c) 02(3−2x)dx  d) 2−1xdx 

Answer | Solution a | Solution b | Solution c | Solution d

Exercise 2.1:2

Calculate the integrals

a) 02(x2+3x3)dx  b) 2−1(x−2)(x+1)dx 
c) 49x−1xdx  d) 14x2xdx 

Answer | Solution a | Solution b | Solution c | Solution d

Exercise 2.1:3

Calculate the integrals

a) sinxdx  b) 2sinxcosxdx 
c) e2x(ex+1)dx  d) xx2+1dx 

Answer | Solution a | Solution b | Solution c | Solution d

Exercise 2.1:4

a) Calculate the area between the curve y=sinx and the x-axis when 0x45.
b) Calculate the area under the curve y=−x2+2x+2 and above the \displaystyle x-axis.
c) Calculate the area of the finite region between the curves \displaystyle y=\frac{1}{4}x^2+2 and \displaystyle y=8-\frac{1}{8}x^2 (Swedish A-level 1965).
d) Calculate the area of the finite region enclosed by the curves \displaystyle y=x+2, y=1 and \displaystyle y=\frac{1}{x}.
e) Calculate the area of the region given by the inequality, \displaystyle x^2\le y\le x+2.

Answer | Solution a | Solution b | Solution c | Solution d | Solution e

Exercise 2.1:5

Calculate the integral

a) \displaystyle \displaystyle \int \displaystyle\frac{dx}{\sqrt{x+9}-\sqrt{x}}\quad (HINT: multiply the top and bottom by the conjugate of the denominator)
b) \displaystyle \displaystyle \int \sin^2 x\ dx\quad (HINT: rewrite the integrand using a trigonometric formula)

Answer | Solution a | Solution b

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/2.1_%C3%9Cbungen“