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2.1 Übungen

Aus Online Mathematik Brückenkurs 2

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|width="50%"| <math>\displaystyle\int_{-1}^{2}|x| \, dx</math>
|width="50%"| <math>\displaystyle\int_{-1}^{2}|x| \, dx</math>
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</div>{{#NAVCONTENT:Answer|Answer 2.1:1|Solution a|Solution 2.1:1a|Solution b|Solution 2.1:1b|Solution c|Solution 2.1:1c|Solution d|Solution 2.1:1d}}
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</div>{{#NAVCONTENT:Antwort|Antwort 2.1:1|Solution a|Solution 2.1:1a|Solution b|Solution 2.1:1b|Solution c|Solution 2.1:1c|Solution d|Solution 2.1:1d}}
===Übung 2.1:2===
===Übung 2.1:2===
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|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>
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</div>{{#NAVCONTENT:Answer|Answer 2.1:2|Solution a|Solution 2.1:2a|Solution b|Solution 2.1:2b|Solution c|Solution 2.1:2c|Solution d|Solution 2.1:2d}}
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</div>{{#NAVCONTENT:Antwort|Antwort 2.1:2|Solution a|Solution 2.1:2a|Solution b|Solution 2.1:2b|Solution c|Solution 2.1:2c|Solution d|Solution 2.1:2d}}
===Übung 2.1:3===
===Übung 2.1:3===
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|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>
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</div>{{#NAVCONTENT:Answer|Answer 2.1:3|Solution a|Solution 2.1:3a|Solution b|Solution 2.1:3b|Solution c|Solution 2.1:3c|Solution d|Solution 2.1:3d}}
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</div>{{#NAVCONTENT:Antwort|Antwort 2.1:3|Solution a|Solution 2.1:3a|Solution b|Solution 2.1:3b|Solution c|Solution 2.1:3c|Solution d|Solution 2.1:3d}}
===Übung 2.1:4===
===Übung 2.1:4===
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|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>.
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</div>{{#NAVCONTENT:Answer|Answer 2.1:4|Solution a|Solution 2.1:4a|Solution b|Solution 2.1:4b|Solution c|Solution 2.1:4c|Solution d|Solution 2.1:4d|Solution e|Solution 2.1:4e}}
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</div>{{#NAVCONTENT:Antwort|Antwort 2.1:4|Solution a|Solution 2.1:4a|Solution b|Solution 2.1:4b|Solution c|Solution 2.1:4c|Solution d|Solution 2.1:4d|Solution e|Solution 2.1:4e}}
===Übung 2.1:5===
===Übung 2.1:5===
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|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)
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</div>{{#NAVCONTENT:Answer|Answer 2.1:5|Solution a|Solution 2.1:5a|Solution b|Solution 2.1:5b}}
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</div>{{#NAVCONTENT:Antwort|Antwort 2.1:5|Solution a|Solution 2.1:5a|Solution b|Solution 2.1:5b}}

Version vom 13:29, 10. Mär. 2009

       Theorie          Übungen      

Übung 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 

Antwort | Solution a | Solution b | Solution c | Solution d

Übung 2.1:2

Calculate the integrals

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

Antwort | Solution a | Solution b | Solution c | Solution d

Übung 2.1:3

Calculate the integrals

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

Antwort | Solution a | Solution b | Solution c | Solution d

Übung 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 x-axis.
c) Calculate the area of the finite region between the curves y=41x2+2 and y=8−81x2 (Swedish A-level 1965).
d) Calculate the area of the finite region enclosed by the curves y=x+2y=1 and y=x1.
e) Calculate the area of the region given by the inequality, x2yx+2.

Antwort | Solution a | Solution b | Solution c | Solution d | Solution e

Übung 2.1:5

Calculate the integral

a) dxx+9−x  (Hint: multiply the top and bottom by the conjugate of the denominator)
b) sin2x dx  (Hint: rewrite the integrand using a trigonometric formula)

Antwort | Solution a | Solution b

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