According to Fractional calculus , the formula is \dfrac{1}{\Gamma (a)} \int_{0}^{x} (x - t)^{a - 1} f(t) dt. a = 2 corresponds to the half integral. The equation is just \int_{0}^{x} (x - t) sinh(t) dt = ...

The solution is not correct. It begins well, our probability is the probability Chicago wins in 7, plus the probability New York wins in 7. We find the probability Chicago wins in 7, and leave ...

One approach would be to do it using Newton's method. We want to solve the equation f(h)=0, with f(h) = L\left( r^2 \arccos \left(\frac{h}{r}\right) - h\sqrt{r^2-h^2} \right) - V With Newton's ...

From the Archimedes principal we know that the object will displace the water of same mass as it. So the object will displace 500kg water and 500kg water = 0.5m3 water. We also know that the lost ...

Your logic is incorrect. Let us see why. For example, your logic would tell you : The opposite of "it did not rain this week" is "it rained on all days this week". That is not true. The opposite of ...

I think that the wikipedia article about Bayes factor presents an example at the end that is exactly the same as yours ( https://en.wikipedia.org/wiki/Bayes_factor ). This is how I understand it and ...