Today's calculation of Integral 301
Source: 2800 Waseda University entrance exam/Science and Technology
February 17, 2008
calculusintegrationgeometrygeometric transformationrotationcalculus computations
Problem Statement
For the positive constant number , let be the part surrounded by the curve \sqrt{x}\plus{}\sqrt{y}\equal{}\sqrt{a} and the line x\plus{}y\equal{}a.
(1) Draw the outline of and find the area.
(2) Find the volume of the solid by rotating about the line x\plus{}y\equal{}a as the rotation axis.