If

$\displaystyle\int_{0}^{\infty} \sin x^7\ dx = \sin \left(\frac{\pi}{a}\right)\Gamma\left({\frac{b}{7}}\right)$

Find $\boxed{a+b}$

Try my set

The answer is 22.

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Which is the same as (sin(pi/2n)*Gamma(1/n))/n

Vijay Simha
- 3 years, 9 months ago

@Aman Rajput Can u please proof the identity

A Former Brilliant Member
- 3 years, 1 month ago

Well, again overrated!

Just use the fact that $sin({x}^{7}) = \frac{{e}^{i{x}^{7}} - {e}^{-i{x}^{7}}}{2i}$

and then just some bashing you are done with the answer.

2 Helpful
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0 Brilliant
0 Confused

So u actually solved it ? Try guessing your way out too sometimes :P

A Former Brilliant Member
- 6 years, 2 months ago

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I see that you actually trolled us only. I was right! You are here, you will be here!

Kartik Sharma
- 6 years, 2 months ago

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No no . Actually today in the morning (6:37 am) to be precise , I got an email from Pranjal . So while talking , I told him that today was my free day and I told him I would be solving his set "My CS Problems" but I just wandered off and started with Calculus first .

So I was solving questions for abt an hour or so and now I am entering the answers . 12 more to go ! Hmpf!

A Former Brilliant Member
- 6 years, 2 months ago

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@A Former Brilliant Member – Sir Prince, please could you check the email I had sent you?

User 123
- 6 years, 2 months ago

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@User 123 – Well , I have replied long ago ...

A Former Brilliant Member
- 6 years, 2 months ago

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@A Former Brilliant Member – Sorry, I just saw that. Sorry!

User 123
- 6 years, 2 months ago

@A Former Brilliant Member – Hmm I see. Well, I was counting chickens before they are hatched then. Sorry!

Kartik Sharma
- 6 years, 2 months ago

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Use this :

$\displaystyle \int\limits_0^{\infty} \sin(x^n)dx = \sin(\frac{\pi}{2n})\Gamma(\frac{n+1}{n})$

And you will get $\boxed{22}$ .