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2.2 Übungen

Aus Online Mathematik Brückenkurs 2

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K (Robot: Automated text replacement (-Övningar +Exercises))
K (Robot: Automated text replacement (-Svar +Answer))
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|width="100%"| <math>\displaystyle \int x^2 e^{x^3} \, dx\quad</math> by using the substitution <math>u=x^3</math>.
|width="100%"| <math>\displaystyle \int x^2 e^{x^3} \, dx\quad</math> by using the substitution <math>u=x^3</math>.
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</div>{{#NAVCONTENT:Answer|Svar 2.2:1|Solution a|Lösning 2.2:1a|Solution b|Lösning 2.2:1b|Solution c|Lösning 2.2:1c}}
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</div>{{#NAVCONTENT:Answer|Answer 2.2:1|Solution a|Lösning 2.2:1a|Solution b|Lösning 2.2:1b|Solution c|Lösning 2.2:1c}}
===Exercise 2.2:2===
===Exercise 2.2:2===
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|width="50%"| <math>\displaystyle\int_{0}^{1} \sqrt[\scriptstyle3]{1 - x}\, dx</math>
|width="50%"| <math>\displaystyle\int_{0}^{1} \sqrt[\scriptstyle3]{1 - x}\, dx</math>
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</div>{{#NAVCONTENT:Answer|Svar 2.2:2|Solution a|Lösning 2.2:2a|Solution b|Lösning 2.2:2b|Solution c|Lösning 2.2:2c|Solution d|Lösning 2.2:2d}}
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</div>{{#NAVCONTENT:Answer|Answer 2.2:2|Solution a|Lösning 2.2:2a|Solution b|Lösning 2.2:2b|Solution c|Lösning 2.2:2c|Solution d|Lösning 2.2:2d}}
===Exercise 2.2:3===
===Exercise 2.2:3===
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|width="50%"| <math>\displaystyle\int \displaystyle\frac{\sin \sqrt{x}}{\sqrt{x}}\, dx</math>
|width="50%"| <math>\displaystyle\int \displaystyle\frac{\sin \sqrt{x}}{\sqrt{x}}\, dx</math>
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</div>{{#NAVCONTENT:Answer|Svar 2.2:3|Solution a|Lösning 2.2:3a|Solution b|Lösning 2.2:3b|Solution c|Lösning 2.2:3c|Solution d|Lösning 2.2:3d|Solution e|Lösning 2.2:3e|Solution f|Lösning 2.2:3f}}
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</div>{{#NAVCONTENT:Answer|Answer 2.2:3|Solution a|Lösning 2.2:3a|Solution b|Lösning 2.2:3b|Solution c|Lösning 2.2:3c|Solution d|Lösning 2.2:3d|Solution e|Lösning 2.2:3e|Solution f|Lösning 2.2:3f}}
===Exercise 2.2:4===
===Exercise 2.2:4===
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|width="50%"| <math>\displaystyle\int \frac{x^2}{x^2 +1}\, dx</math>
|width="50%"| <math>\displaystyle\int \frac{x^2}{x^2 +1}\, dx</math>
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</div>{{#NAVCONTENT:Answer|Svar 2.2:4|Solution a|Lösning 2.2:4a|Solution b|Lösning 2.2:4b|Solution c|Lösning 2.2:4c|Solution d|Lösning 2.2:4d}}
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</div>{{#NAVCONTENT:Answer|Answer 2.2:4|Solution a|Lösning 2.2:4a|Solution b|Lösning 2.2:4b|Solution c|Lösning 2.2:4c|Solution d|Lösning 2.2:4d}}

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Exercise 2.2:1

Calculate the integrals

a) 12dx(3x−1)4  by using the substitution u=3x−1,
b) (x2+3)5xdx  by using the substitution u=x2+3,
c) x2ex3dx  by using the substitution u=x3.

Answer | Solution a | Solution b | Solution c

Exercise 2.2:2

Calculate the integrals

a) 0cos5xdx  b) 012e2x+3dx 
c) 053x+1dx  d) 0131−xdx 

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

Exercise 2.2:3

Calculate the integrals

a) 2xsinx2dx  b) sinxcosxdx 
c) xlnxdx  d) x+1x2+2x+2dx 
e) 3xx2+1dx  f) xsinxdx 

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

Exercise 2.2:4

Use the formula

dxx2+1=arctanx+C 

to calculate the integrals

a) dxx2+4  b) dx(x−1)2+3 
c) dxx2+4x+8  d) x2x2+1dx 

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

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/2.2_%C3%9Cbungen“