Paneer Definite Masala 3

Calculus Level 5

$\large \int_0^\infty \dfrac{ \cos xt}{1+t^2} \, dt$

If the integral above is equal to $\dfrac ab$ , where $a$ and $b$ are coprime positive integers, find $a+b+ab$ .

Take $x=\ln \frac{3\pi}5$

The answer is 41.

1 solution

Akhilesh Vibhute
Mar 6, 2016

Answer is 5/6 Assume the function f(x)=e^-x First apply Fourier transform and then inverse Fourier transform So given Integral equals π/2*e^-x

OK that's nice.A more basic approach would be to use Feynman's Trick.Differentiatiating twice wrt the parameter x would yield a relation of the form $d/dx(dI/dx)=kI$ where $k$ is a positive constant. The solution to this is quite obvious.And we choose a boundary conditions.To get ans ans $π/2e^-b$

Spandan Senapati - 4 years, 1 month ago

Paneer Definite Masala 3

The answer is 41.

1 solution

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