sqrt pi

Why is the area of the circle \ (S = \pi r^2 \)? How to testify?This formula is important because it is the basis for all the volume of the rotating body (cylinder, cone, round table, ball, etc.), it is better to be more rigorous proof, rather than

Sin cos exp is calculated using the Taylor Formula and mclawin formula. To prevent the power operation index from being too high, it is easy to cause overflow when a large input parameter is calculated. Considering that sin and cos both use 2 * PI

Solve $$\int_0^{\frac{\pi}{2}} {{{\ln}^2}\sin XDX} = \int_0^{\frac{\pi}{2}} {{{\ln}^2}\cos XDX} $$ value.Apparently \[\int_0^{\frac{\pi}{2}} {{{\ln}^2}\sin XDX} \underline{\underline {{\text{order}x = \frac{\pi}{2}-t}}} \int_0^{\frac{\ Pi}{2}}

1 ($4 \ times 10' = 40' $) (1) $ \ DPS {\ lim _ {x \ to 0} \ frac {\ SiN x-\ arctan x }{\ Tan x-\ arcsin x }}$. Answer: $ \ beex \ Bea \ lim _ {x \ to 0} \ frac {\ SiN x-\ arctan x} {\ Tan x-\ arcsin x} & = \ lim _ {x \ to 0} \ frac {\ SEZ {X-\ frac

1.(1) solving two curve equations to get the intersection of $ (0,0) $, $ (1,e) $, so the surrounding area\[A= \int_0 ^1 (x e-xe^x) dx= \frac{e}{2} x^2 \bigg|_0^1-x e^x \bigg|_{0}^1 +\int_0^1 e^x DX =\frac e 2-1.\](Note: When $0(2) Easy to solve the

    1. find $ \ DPS {\ int _ \ VGA y ^ 2 \ RD s} $, $ \ VGA $ consists of $ \ DPS {\ sedd {\ BA {RL} x ^ 2 + y ^ 2 + Z ^ 2 & = a ^ 2 \ x + Z & = A \ EA }}$ decision. Answer: $ \ VGA $: $ \ Bex \ sedd {\ BA {RL} \ sex {X-\ cfrac {A} {2} ^ 2 + y ^ 2 +

Pi is an irrational number, and there is no precise formula to calculate the π value, and π can only be calculated using approximate algorithms.The internationally recognized PI values are calculated using the Monte Carlo method.Monte Carlo (Monte

usingSystem;usingSystem.Math;namespacepiwithmontecarlo{/// ///Trivial, synchronous calculation algorithm/// Public Static classTrivialpicalculator { Public Static DoubleCalculate (intiterations) { intInCircle =0; varRandom

 /***************************************************function* Calculate pi by probability method and cutting methodDescription* Probability method requires a number of points not in the input circle* The number of cuts required for the cutting

The purpose of this article is to let oneself learn Goldbach conjecture study of specific methods, specific reference Pan book "Prime Distribution and Goldbach conjecture", in this I will prove the details as far as possible to write more detailed,