- #1

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## Homework Statement

How to integrate:

## Homework Equations

## The Attempt at a Solution

I used formula: sin^2(t) = ( 1-cos^2(t))

and now it's:

Then:

u=cos(t)

du=-sin(t)

What to do next?

Last edited:

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- Thread starter evol_w10lv
- Start date

- #1

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How to integrate:

I used formula: sin^2(t) = ( 1-cos^2(t))

and now it's:

Then:

u=cos(t)

du=-sin(t)

What to do next?

Last edited:

- #2

arildno

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[tex]-6\sqrt{s^{2}+1}, s=\frac{\sqrt{5}u}{2}[/tex]

Now, utilize the trigonometric identity:

[tex]\tan^{2}(y)+1=\frac{1}{\cos^{2}(y)}[/tex]

in a creative way.

- #3

CAF123

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Try using the identity 1 + tan

- #4

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Maybe I have to use polar coordinates? Any sugestions? Before I tried with diferent way, but I guess that integration without polar coordinates is too hard.

- #5

arildno

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- #6

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Seems to me that variant when we use y=y(x) is more complicated than variant with polar coordinates.

[tex]-6\sqrt{s^{2}+1}, s=\frac{\sqrt{5}u}{2}[/tex]

Now, utilize the trigonometric identity:

[tex]\tan^{2}(y)+1=\frac{1}{\cos^{2}(y)}[/tex]

in a creative way.

Not clear, how did you get there: [tex]s=\frac{\sqrt{5}u}{2}[/tex]

We didn't learn about triple substitution, but I want to understand, how to get the final result. Can you explain some how?

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