(a)[4]
Show that $b = 3a$ using the information given.
(b)[7]
Show that the shaded region between the line and the curve has area $ka^4$, where $k$ is the fraction to be found.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
The sketch displays a section of the curve with equation $y = x^3 - 2bx^2 + b^2x$ together with the line $OA$, and $A$ is the maximum point on the curve. The $x$-coordinate of $A$ is $a$, and the curve also has a minimum point at $(b, 0)$, where $a$ and $b$ are positive constants.