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## anonymous 5 years ago Find the laplace transform of f(t) = cos(wt) using direct integration. Thanks guys! Just confused on what to do when using integration by parts, since we have two continious functions of t. >>> exp(-st) and cos(wt) <<<< we constantly need to use integration by parts and it's confusing me! I've read up on Eulers Identity, but i'm not sure how to actually apply it.

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1. anonymous

you decompose coswt into e^jwt+e^-jwt/2 it will help you

2. anonymous

So how did you actually get that?

3. anonymous

m doing...

4. anonymous

$\int\limits_{0}^{\infty}(e ^{jwt}+e ^{-jet})e ^{-st}dt/2$=$0.5[e ^{jwt-st}]/(jwt-st)-[e ^{-jwt-st}]/(jwt+st)|_{0}^{\infty}$ 1/2(jw+s)+(1/2(s-jw))=s/(s^2+w^2)

5. anonymous

Yep I understand all that.. It's just why did you change cos(wt) to the (e^jwt+e^−jwt)

6. anonymous

/2

7. anonymous

ggabnore are u there?

8. anonymous

yes

9. anonymous

the decomposition of coswt comes from Eular's formula.

10. anonymous

e^(jwt) = cos(wt) + jsin(wt), j=√(-1) thats euler identity, how does it become... cos(wt) = e(jwt) + e(-jwt)

11. anonymous

e^(-jwt)=cos(-wt)+jsin(-wt) =coswt-jsinwt add e^(jwt) and e^(-jwt) then sinwt cancels so you get only 2coswt

12. anonymous

OH I seee. makes sense.. Thanks alot!

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