Today's calculation of Integral 455
Source: 2009 Chiba University entrance exam/Medical
June 24, 2009
calculusintegrationlimittrigonometrycalculus computations
Problem Statement
(1) Evaluate \int_1^{3\sqrt{3}} \left(\frac{1}{\sqrt[3]{x^2}}\minus{}\frac{1}{1\plus{}\sqrt[3]{x^2}}\right)\ dx.
(2) Find the positive real numbers such that for \lim_{t\rightarrow \infty} \left(\int_1^t \frac{1}{1\plus{}\sqrt[3]{x^2}}\ dx\minus{}at^b\right) converges.