Processing Math: Done
2.1 Übungen
Aus Online Mathematik Brückenkurs 2
(Unterschied zwischen Versionen)
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| - | |width="100%"| <math>\displaystyle \int \displaystyle\frac{dx}{\sqrt{x+9}-\sqrt{x}}\quad</math> ( | + | |width="100%"| <math>\displaystyle \int \displaystyle\frac{dx}{\sqrt{x+9}-\sqrt{x}}\quad</math> (Hint: multiply the top and bottom by the conjugate of the denominator) |
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|b) | |b) | ||
| - | |width="100%"| <math>\displaystyle \int \sin^2 x\ dx\quad</math> ( | + | |width="100%"| <math>\displaystyle \int \sin^2 x\ dx\quad</math> (Hint: rewrite the integrand using a trigonometric formula) |
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</div>{{#NAVCONTENT:Answer|Answer 2.1:5|Solution a|Solution 2.1:5a|Solution b|Solution 2.1:5b}} | </div>{{#NAVCONTENT:Answer|Answer 2.1:5|Solution a|Solution 2.1:5a|Solution b|Solution 2.1:5b}} | ||
Version vom 10:55, 28. Okt. 2008
| Theory | Exercises |
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 |
