Processing Math: Done
2.1 Übungen
Aus Online Mathematik Brückenkurs 2
(Unterschied zwischen Versionen)
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 | + | {{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: | + | </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: | + | </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: | + | </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: | + | </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: | + | </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
|
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) | 2−1 xdx |
Answer | Solution a | Solution b | Solution c | Solution d
Laden...Exercise 2.1:2
Calculate the integrals
| a) | 02(x2+3x3)dx | b) | 2−1(x−2)(x+1)dx |
| c) | 49  x−1x dx | 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  x45 |
| b) | Calculate the area under the curve |
| c) | Calculate the area of the finite region between the curves |
| d) | Calculate the area of the finite region enclosed by the curves  y=1 |
| e) | Calculate the area of the region given by the inequality, yx+2 |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e
Exercise 2.1:5
Calculate the integral
| a) | dxx+9−x |
| b) | sin2x dx |
