Evaluate the integral $\int\limits_0^1 {\frac{{{x^4}{{(1 – x)}^4}}}{{1 + {x^2}}}} dx$ and hence prove that $\pi < \frac {22}{7}$.

Solution [.pdf]

Solution [.pdf]

To what maximum radius should earth be compressed so that nothing on earth can escape earth? $[M=6.0\times 10^{24} kg]$

(A) 4.5 mm
(B) 8.9 cm
(C) 8.9 m
(D) 8.9 mm

Solution

Solution [.pdf]