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Find the value of the following integral:

\[ \displaystyle\int_{0}^{\infty} \dfrac{1}{x} \left(\tan^{-1} \pi x - \tan^{-1}x\right)dx.\]

If the following integral is satisfied for some relationship between the constants \(a , b\) and \(c\)-

\[ \displaystyle\int_{-∞}^{∞}\displaystyle\int_{-∞}^{∞} e^{-(ax^{2} + 2bxy + cy^{2})}dxdy = 1\]

Find the ...

The volume of the region of space satisfying all of the following inequalities:

...

If

Hello Friends, its been a long time since I was last active at Brilliant. Actually it was before my JEE exam, and after that i just could not find enough ...

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