Today's calculation of Integral 558
Source: 2010 Keio University entrance exam/Pharmacy
February 17, 2010
calculusintegrationquadraticsfunctioninequalitiesalgebracalculus computations
Problem Statement
For a positive constant , let be the roots of the quadratic equation x^2 \plus{} t^2x \minus{} 2t \equal{} 0.
Find the minimum value of \int_{ \minus{} 1}^2 \left\{\left(x \plus{} \frac {1}{\alpha ^ 2}\right)\left(x \plus{} \frac {1}{\beta ^ 2}\right) \plus{} \frac {1}{\alpha \beta}\right\}dx.