$V$ denotes real vector space $V$ consisting of all polynomials with real coefficients/any degree so $V$ is infinite dimensional. A symmetric bilinear form is defined on V by
$(f,g) = \int_0^\infty f(x)g(x)e^{-x} dx$
i) State briefly why this is positive definite on $V$ (may quote any general property of real integrals).