Question

Euler’s integral of the first kind, which is a proper integral, is used to define the gamma function.

(a) True

(b) False

The question was asked in examination.

This is a very interesting question from Transformation (Reduction) of Quadratic Form to Canonical Form in section Eigen Values and Eigen Vectors of Engineering Mathematics

Answer 1

Right choice is (b) False

Best explanation: Euler’s integral of the second kind, which is an improper function, is used to define gamma function for integer x>0.

\(Γ(x)= ∫_0^∞ t^{x-1}e^{-t}.dt \)