MathDB

1.Let x \equal{} \alpha ,\ \beta \ (\alpha < \beta ) are

x

coordinates of the intersection points of a parabola y \equal{} ax^2 \plus{} bx \plus{} c\ (a\neq 0) and the line y \equal{} ux \plus{} v. Prove that the area of the region bounded by these graphs is \boxed{\frac {|a|}{6}(\beta \minus{} \alpha )^3}. 2. Let x \equal{} \alpha ,\ \beta \ (\alpha < \beta ) are

x

coordinates of the intersection points of parabolas y \equal{} ax^2 \plus{} bx \plus{} c and y \equal{} px^2 \plus{} qx \plus{} r\ (ap\neq 0). Prove that the area of the region bounded by these graphs is \boxed{\frac {|a \minus{} p|}{6}(\beta \minus{} \alpha )^3}.

Problem Statement