Today's calculation of Integral 502
Source: National Defence Medical College entrance exam, Problem 2 2009/10/31
November 5, 2009
calculusintegrationlimitcalculus computations
Problem Statement
(1) For , prove that (\sqrt {2} \minus{} 1)x \plus{} 1 < \sqrt {x \plus{} 1} < \sqrt {2}.
(2) Find \lim_{a\rightarrow 1 \minus{} 0} \frac {\int_a^1 x\sqrt {1 \minus{} x^2}\ dx}{(1 \minus{} a)^{\frac 32}}.