MCQ
$\int_0^\infty {\frac{{{x^3}\,dx}}{{{{({x^2} + 4)}^2}}} = } $
- A$0$
- ✓$\infty $
- C$\frac{1}{2}$
- DNone of these
$ = \frac{1}{2}\int_0^\infty {\frac{t}{{{{(t + 4)}^2}}}dt} $,
[Putting ${x^2} = t$]
$ = \frac{1}{2}\int_0^\infty {\left[ {\frac{1}{{t + 4}} - \frac{4}{{{{(t + 4)}^2}}}} \right]dt = \frac{1}{2}\left[ {\log (t + 4) + \frac{4}{{t + 4}}} \right]_0^\infty } $
$ = \frac{1}{2}\left[ {\log \infty + 0 - (\log 4 + 1)} \right] = \infty $.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.