- #1

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hope anybody can help me with a tricky integral ( i should check if it exists):

[tex]\int_{0}^{\frac{\pi}{2}} \frac{1}{\sqrt{sin(x)}*cos^2(x)} dx[/tex]

And i have really no idea where to start!

thanks

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- Thread starter heinerL
- Start date

- #1

- 19

- 0

hope anybody can help me with a tricky integral ( i should check if it exists):

[tex]\int_{0}^{\frac{\pi}{2}} \frac{1}{\sqrt{sin(x)}*cos^2(x)} dx[/tex]

And i have really no idea where to start!

thanks

- #2

Dick

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- #4

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And yeah, i know i did check it with maple too!

- #5

vela

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- #6

ideasrule

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So you mean, because it does not exist for Pi/2 it does not exist at all? so simple?

That's not necessarily true. Consider the integral of 1/sqrt(x) from x=0 to 1. The integral exists, even though 1/sqrt(x) itself does not exist at x=0.

- #7

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But if I try the limit x->Pi/2 i still get inf?

- #8

Dick

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But if I try the limit x->Pi/2 i still get inf?

The easiest way to see the problem at pi/2 is to expand your integrand in a Taylor series around x=pi/2 and realize the integrand looks like 1/y^2 where y=pi/2-x.

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- #10

Dick

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