An Integral from the MIT Integration Bee

#Integrals #Math #MIT

Here is the solution to an integral problem in the MIT Integration Bee Competition.

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I share Maths problems and Maths topics from well-known contests, exams and also from viewers around the world. Apart from sharing solutions to these problems, I also share my intuitions and first thoughts when I tried to solve these problems.

[subhajitdas]

If you use the substitution z=x^4, and then use gamma function..then the integral reduces  Γ(3/2)/4 = √π/8.. done😁

[infiniusnobelliusroy]

Simple substitute and u will get gamma function..solved in one minute

[niceroundtv]

5:48 the limit as x->inf is an indeterminate form. It does approach 0, as stated.

[toothpastedinnr]

it's easy with change of variables and gamma function

[mackenziekelly]

I would have done integration by parts first. u=x^2 and dv=x^3e^(-x^4)dx. dv has obvious integral, uv term goes to zero then you get 1/2 integral of xe^(-x^4). Now make your substitution s=x^2 to give you your classic gamma integral. Maybe it's just me, but it seemed more natural for me than substituting first

[shreyaskali]

The rule is ILATE I think instead of LIATE.

[amiyancandol]

If use of gamma function is allowed then it becomes 1/4 gamma 3/2 which is √π/8.. without that idk I'm noob 😎

[neilgerace]

The integral I, the Gaussian integral, has a standard result sqrt(π) so in the integration bee can you just write that?

[ΓιώργοςΚοτσάλης-ση]

Wouldnt the first sub to try be u=x^2, v=e^-x^2 ?

[manojsurya]

Ok in comments everyone is saying some method with gamma function, can anyone explain pls

[leif]

WAIT x/2 times e^-× you have infinty times zero when you plug in infinty so you dont know the answer to that..

[mathevengers]

Here's link to an amazing Math video:

[mathevengers]

Here's link to an amazing Math video: