Since I don't know the solutions to all of these, I'm posting them here instead of in the Math Challenge Problems forum.

None of these integrals should have very complicated solutions.

EDIT: The fourth one might be too easy.

1)

2)

3)

4)

5)

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- February 7th 2010, 06:33 PMRandom Variablea few more integrals from this year's MIT Integration Bee
Since I don't know the solutions to all of these, I'm posting them here instead of in the Math Challenge Problems forum.

None of these integrals should have very complicated solutions.

EDIT: The fourth one might be too easy.

1)

2)

3)

4)

5) - February 7th 2010, 06:56 PMfelper

I think that it's ok (Sleepy) - February 7th 2010, 07:00 PMfelper
The fourth:

Let be , then

- February 7th 2010, 07:00 PMRandom Variable
- February 7th 2010, 07:10 PMvince
4)

=

let u =

= - February 7th 2010, 07:14 PMvince
- February 7th 2010, 07:27 PMfelper

Let be

Let be then:

Which is the Laplace Transform for cos(2t), so, the integral is

End. - February 7th 2010, 08:07 PMfelper

- February 7th 2010, 08:50 PMRandom Variable
- February 7th 2010, 10:42 PMGeneral
Do you have a website for thier problems?

- February 8th 2010, 05:32 AMvince

Choose

=

Choose

=

=

=

=

The last 2 terms evaluate to 0.

=

All in all, quite a yawner of a set. The one where Felper recognized the Laplace was the best one, but even that one was str8tforward. This must be for the total newbie undergrads at mit.