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A block of mass \(m\) can slide freely in a slot made in a bigger block of mass \(M,\) as shown in the diagram above. There is no friction anywhere ...

\[\large\int_{-\sqrt3}^{\sqrt3}\sqrt{4-x^2}\,dx=\dfrac{A\pi}{B}+{\sqrt{B}}\]

If the equation above holds true for integers \(A\) and \(B\), input your answer as ...

\[\large \int\dfrac{dx}{{\cos^3 x}\sqrt{2\sin(2x)}}\,= {(\tan x)^A} + C{(\tan x)^B}+k \]

The equation above holds true for reals \(A\), \(B\) and ...

\[\large8\int_{0}^{1}\dfrac{\ln{(1+x)}}{1+{x^2}}\,dx=\pi \, {\ln A}\]

Find \(A^2\).

If the curve \(f(x)=2{ x }^{ 3 }+a{ x }^{ 2 }+bx\), where \(a\) and \(b\) are positive integers, cuts the \(x\)-axis at three distinct points. Then find the ...

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