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An integral by parts quesiton

  • Thread starter vande060
  • Start date
  • #1
186
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Homework Statement



I have to solve this integral

S cos(x^1/2)dx

where S is the integral symbol


Homework Equations





The Attempt at a Solution



the book tells me to use substitution and then integrate by parts

so i say u = x^1/2
du = 1/2*x^-1/2

then i can write 2 S (cos(u)du)/ x^1/2

where S in the integral sign

from here i think i can substitute the x^1/2 in the denominator by u because of the definition u = x^1/2

after the last substitution my integral would look like 2 S cos(u)/u

is this even close to right
 

Answers and Replies

  • #2
dextercioby
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Homework Statement



I have to solve this integral

S cos(x^1/2)dx

where S is the integral symbol


Homework Equations





The Attempt at a Solution



the book tells me to use substitution and then integrate by parts

so i say u = x^1/2
du = 1/2*x^-1/2 dx

then i can write 2 S (cos(u)du)/ x^1/2

where S in the integral sign

from here i think i can substitute the x^1/2 in the denominator by u because of the definition u = x^1/2

after the last substitution my integral would look like 2 S cos(u)/u du

is this even close to right
There. Fixed the missing part. You'll never get an elementary function instead of the question mark below

[tex] \int\frac{\cos u}{u} {}du= ? + C [/tex]

However, the computation you made is wrong. <u> should be in the numerator, so the <exotic> part won't apply.
 
Last edited:
  • #3
[tex]t=\sqrt{x} \implies t^2=x \implies 2tdt=dx[/tex]

Your integral will be :

[tex]2 \int \, t \, cos(t) \, dt[/tex]

A quick application of integration by parts will kill it.
 
  • #4
186
0
[tex]t=\sqrt{x} \implies t^2=x \implies 2tdt=dx[/tex]

Your integral will be :

[tex]2 \int \, t \, cos(t) \, dt[/tex]

A quick application of integration by parts will kill it.
oh wow i didnt even think of that, good suggestion and thank you. i can finish the integration by parts no problem
 

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