2.3 Exercises

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(Ny sida: ===Övning 2.2:2=== <div class="ovning"> Beräkna integralerna {| width="100%" cellspacing="10px" |a) |width="50%"|<math>\displaystyle\int_{0}^{\pi} \cos 5x\, dx</math> |b) |width="50%"|...)
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{| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
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| style="border-bottom:1px solid #000" width="5px" | &nbsp;
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{{Not selected tab|[[2.3 Integration by parts|Theory]]}}
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{{Selected tab|[[2.3 Exercises|Exercises]]}}
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| style="border-bottom:1px solid #000" width="100%"| &nbsp;
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===Exercise 2.3:1===
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<div class="ovning">
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Calculate the integrals
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{| width="100%" cellspacing="10px"
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|a)
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|width="50%"|<math>\displaystyle\int 2x e^{-x} \, dx</math>
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|b)
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|width="50%"| <math>\displaystyle\int(x+1) \sin x \, dx</math>
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|-
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|c)
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|width="50%"| <math> \displaystyle\int x^2 \cos x \, dx</math>
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|d)
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|width="50%"| <math>\displaystyle\int x \ln x \, dx</math>
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|}
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</div>{{#NAVCONTENT:Answer|Answer 2.3:1|Solution a|Solution 2.3:1a|Solution b|Solution 2.3:1b|Solution c|Solution 2.3:1c|Solution d|Solution 2.3:1d}}
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===Exercise 2.3:2===
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===Övning 2.2:2===
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<div class="ovning">
<div class="ovning">
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Beräkna integralerna
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Calculate the integrals
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|width="50%"|<math>\displaystyle\int_{0}^{\pi} \cos 5x\, dx</math>
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|width="50%"|<math>\displaystyle\int e^{\sqrt x}\, dx</math>
|b)
|b)
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|width="50%"| <math>\displaystyle\int_{0}^{1/2} e^{2x+3}\, dx</math>
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|width="50%"| <math>\displaystyle\int_{0}^{1} x^3 e^{x^2} \, dx</math>
|-
|-
|c)
|c)
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|width="50%"| <math> \displaystyle\int_{0}^{5} \sqrt{3x + 1} \, dx</math>
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|width="50%"| <math> \displaystyle\int \tan x \, dx</math>
|d)
|d)
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|width="50%"| <math>\displaystyle\int_{0}^{1} \sqrt[\scriptstyle3]{1 - x}\, dx</math>
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|width="50%"| <math>\displaystyle\int \ln x\, dx</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 2.2:2|Lösning a|Lösning 2.2:2a|Lösning b|Lösning 2.2:2b|Lösning c|Lösning 2.2:2c|Lösning d|Lösning 2.2:2d}}
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</div>{{#NAVCONTENT:Answer|Answer 2.3:2|Solution a|Solution 2.3:2a|Solution b|Solution 2.3:2b|Solution c|Solution 2.3:2c|Solution d|Solution 2.3:2d}}

Current revision

       Theory          Exercises      

Exercise 2.3:1

Calculate the integrals

a) \displaystyle \displaystyle\int 2x e^{-x} \, dx b) \displaystyle \displaystyle\int(x+1) \sin x \, dx
c) \displaystyle \displaystyle\int x^2 \cos x \, dx d) \displaystyle \displaystyle\int x \ln x \, dx
Answer
Answer 2.3:1
Solution a
Solution 2.3:1a
Solution b
Solution 2.3:1b
Solution c
Solution 2.3:1c
Solution d
Solution 2.3:1d

Exercise 2.3:2

Calculate the integrals

a) \displaystyle \displaystyle\int e^{\sqrt x}\, dx b) \displaystyle \displaystyle\int_{0}^{1} x^3 e^{x^2} \, dx
c) \displaystyle \displaystyle\int \tan x \, dx d) \displaystyle \displaystyle\int \ln x\, dx
Answer
Answer 2.3:2
Solution a
Solution 2.3:2a
Solution b
Solution 2.3:2b
Solution c
Solution 2.3:2c
Solution d
Solution 2.3:2d
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