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Consider a circle with a starting circumference of \(C_0 = 100\) units. Suppose you start on a point on that circle and proceed to walk along it until you take your ...

Let \(C\) be a circle of unit radius centered at the origin, and \( P = (-x_0,0)\) a point outside of it, where \(x_0>1.\) Let \(A\) and \(B\) be the 2 ...

Evaluate the following integral:

\[\large \int_{ - \infty}^{\infty} \frac{\cos x}{1+x^2} dx.\]

Let \(n \in \mathbb{N}_{> 0}\) and consider the binomial expansion of \[(x+y)^n = \sum\limits_{k=0}^{k=n} \alpha_k x^k y^{n-k}\] where ...

\[ \large \dfrac{1}{2 \pi \hbar}\iint\limits_{\mathbb{R}^2} \left (q-\frac{x}{2} \right )ke^{\frac{i}{\hbar}(p-k)x} \, dx dk\]

Let be \(p\), \(q\) are ...

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