Category Archives: IIT JEE
${y_1} = 10\sin \left( {3\pi t + \frac{\pi }{4}} \right)$ & ${y_2} = 5\left[ {\sin (3\pi t) + \sqrt 3 \cos (3\pi t)} \right]$
$U(r)=10r^3$ J
$y = 4{\cos ^2}\left( {\frac{t}{2}} \right)\sin (1000t)$
$\int\limits_0^1 {\frac{{{x^4}{{(1 – x)}^4}}}{{1 + {x^2}}}} dx$
Evaluate the integral $\int\limits_0^1 {\frac{{{x^4}{{(1 – x)}^4}}}{{1 + {x^2}}}} dx$ and hence prove that $\pi < \frac {22}{7}$.
