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`find the length of the curve y=ln(e^{x}+/e^{x}-1) from x=1 to x=2 `


Evaluate ∫0^{π/2a}asinαxdx,α>0 by using Leibniz formula.`


the tunction f(z)= (z)^{2}/z,z≠0  0,z=0  suntistes -Rieman equations at z=0 Does f (0) exist?`


Find the complete integral of xp +3yq = 2(z-x^2.q^2).


Find the complete integral of p3 +q^3 = 27z.


Find the integral surface of x(y^2+z)p-y( x^2+z)q=(x^2-y^2)z through the straight through the x+y = 0,z = 1.


Eliminate the arbitrary function from 2=xy+f(x^2+y^2) to obtain the partial differencial equation.


A composite wall is formed of a 2.5 cm copper plate (k=385 W/m-K). a 3.2 cm layer of

asbestos (k=0.2 W/m-K), and a 5 cm layer of fibreglass (k=0.045 W/m-K). The wall is subjected to an overall temperature drop of 560

∮|z|=1 (z+z̄)dz


The residue at z=2 of the function 2z/(2-z)(z+2) is


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