area between a line and parabola

Practise area between a line and parabola with an original VectorPaths question, worked explanation and related VCE Methods practice.

3 practice marks

Original practice question

Find the exact area enclosed by $y=3x$ and $y=x^2$.

Worked explanation

• Find the intersections

  $x^2=3x$ gives $x=0$ and $x=3$.

• Choose upper minus lower

  On $0<x<3$, $3x>x^2$. Integrate $\int_0^3(3x-x^2)\,dx$.

• Evaluate

  $[\frac{3x^2}{2}-\frac{x^3}{3}]_0^3=\frac{9}{2}$.

Area $=\frac{9}{2}$ square units.

Original VectorPaths practice; not an official VCAA question or marking rubric.