given diameter 25mm
half of the drill point angle =60
cutting velocity=44000mm/minute
length=60mm
feedrate=0.25mm/revolution
determine the time needed to drill a through hole
1) calculate ∫_0 ^(2π) (dt/(cost +x sint)) wih x from R.
2) calculate ∫_0 ^(2π) ((sint)/((cost +xsint)^2 ))dt
3) find[the value of ∫_0 ^(2π) (dt/(cos(2t)+2sin(2t)))
let f(x)=∫_0 ^∞ (t^(a−1) /(x+t^n )) dt with 0<a<1 and x>0 and n≥2
1) determine a explicit form of f(x)
2) calculate g(x) =∫_0 ^∞ (t^(a−1) /((x+t^n )^2 )) dt
3) find f^((k)) (x) at form of integrals
4) calculate ∫_0 ^∞ (t^(a−1) /(9+t^2 )) dt and ∫_0 ^∞ (t^(a−1) /((9+t^2 )^2 ))
5) calculate U_n =∫_0 ^∞ (t^((1/n)−1) /(2^n +t^n )) dt and study the convergence of Σ U_n
let A_n =∫_0 ^∞ (x^(a−1) /(1+x^n ))dx with n integr and n≥2 and 0<a<1
1) calculate A_n
2) find the values of ∫_0 ^∞ (x^(a−1) /(1+x^2 ))dx and ∫_0 ^∞ (x^(a−1) /(1+x^3 ))dx
3)calculate ∫_0 ^∞ (dx/((√x)(1+x^4 ))) and ∫_0 ^∞ (dx/((^3 (√x^2 ))(1+x^4 )))