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## Homework Statement

can som1 please give me an idea where to start with this integral.

integral of: cos (2t) x e^2t

thanx

- Thread starter Chadlee88
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can som1 please give me an idea where to start with this integral.

integral of: cos (2t) x e^2t

thanx

- #2

- 1,707

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well first start with u sub to make it a tad easier

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Dick

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malawi_glenn

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another alternative is to write cos(2t) as exponentials using Eulers forlmulas.

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- 1,707

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and how would you do that?another alternative is to write cos(2t) as exponentials using Eulers forlmulas.

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malawi_glenn

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and how would you do that?

http://upload.wikimedia.org/math/8/d/6/8d662412f1815064827ff58e0280d09c.png

http://upload.wikimedia.org/math/9/8/6/986359d5b505762cd4bb6444081878be.png

http://en.wikipedia.org/wiki/Euler's_formula

- #8

VietDao29

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Whoops, I don't think any Pre-Calculus students do learncan som1 please give me an idea where to start with this integral.

integral of: cos (2t) x e^2t

This is a good candidate for

The formula is:

[tex]\int u dv = uv - \int v du[/tex]

[tex]I = \int e ^ x \sin x dx[/tex]

Let u = e

~~> du = e

[tex]I = \int e ^ x \sin x dx = - e ^ x \cos x + \int e ^ x \cos x dx[/tex]

You should note that, if you let u = e

Let u = e

~~~> du = u = e

We have:

[tex]I = - e ^ x \cos x + \int e ^ x \cos x dx + C' = -e ^ x \cos x + \left( e ^ x \sin x - \int e ^ x \ sin x dx \right) + C' = -e ^ x \cos x + e ^ x \sin x - I + C'[/tex]

Isolate I to one sides yields:

[tex]2I = -e ^ x \cos x + e ^ x \sin x + C'[/tex]

[tex]\Rightarrow I = \frac{1}{2} \left( -e ^ x \cos x + e ^ x \sin x \right) + C[/tex] (where C, and C' are the Constants of Integrations.)

Can you go from here? :)

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