Find a positive constant that satisfies the equation: ∫(1/x²+a²)dx=1    integration limits: [ 0, +∞]    Choose an option: a. a=π/4 b. a=2/π c. a=2π d. a=π/2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find a positive constant that satisfies the equation:

∫(1/x²+a²)dx=1    integration limits: [ 0, +∞] 

 

Choose an option:

a. a=π/4
b. a=2/π
c. a=2π
d. a=π/2
Encontre uma constante positiva a que satisfaz a equacão
dz =1
Escolha uma opcão:
O aa=
O b.a =
Oca= 2x
O da=
Transcribed Image Text:Encontre uma constante positiva a que satisfaz a equacão dz =1 Escolha uma opcão: O aa= O b.a = Oca= 2x O da=
Expert Solution
Step 1

Consider the equation 01x2+a2dx=1

We have to find the value of a

Use integral formula 1x2+a2dx=1atan1xa+c

Hence,

01x2+a2dx=11atan1xa0=1

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