Question
Evaluate the following integrals as a limit of a sum.
$\int_0^4 x^2 d x$
$\int_0^4 x^2 d x$
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$\frac{\left(x^2+2 x+2\right)^{\frac{3}{2}}}{(\sqrt{x}+3)^3(\cos x)^x}$
$\sin ^2\left[\cot ^{-1}\left(\sqrt{\frac{1+x}{1-x}}\right)\right]$