The value of $$\int_0^{\pi /4} {x\cos \left( {{x^2}} \right)dx} $$ correct to three decimal places (assuming that $$\pi = 3.14$$ ) is ________.

The value of $$\mathop {\lim }\limits_{x \to 1} {{{x^7} - 2{x^5} + 1} \over {{x^3} - 3{x^2} + 2}}.$$

If for non-zero $$x,$$ $$af\left( x \right) + bf\left( {{1 \over x}} \right) = {1 \over x} - 25$$
where $$a \ne b$$ then $$\int\limits_1^2 {f\left( x \right)dx} \,$$ is

$$\,\int\limits_{1/\pi }^{2/\pi } {{{\cos \left( {1/x} \right)} \over {{x^2}}}dx = } $$ __________.