(i)Suppose that a, b and t are positive. Which of
the following two expressions is the larger P=\left(\int_0^t
x^{a+b}dx\right)^2, \qquad Q=\left(\int_0^t x^{2a}dx \right)
\left(\int_0^t x^{2b}dx\right)\ ? (ii)By considering
the inequality \int_0^t [f(x)+\lambda g(x)]^2 dx \geq 0, prove
that, for all functions f(x) and g(x), \left(\int_0^t
f(x)g(x)dx\right)^2 \leq \left(\int_0^t f(x)^2 dx\right)
\left(\int_0^t g(x)^2 dx\right).