Definite integrals and area under a curveEdexcel A-Level Maths: Mind map

Exam questions on Definite integrals and area under a curve

1. The curve $C$ has equation $y=x^2-4x+3$.
   Find the total area bounded by $C$, the $x$-axis and the lines $x=0$ and $x=4$.2 marks
2. The curve $C$ has equation $y=6x-x^2$ and the line $l$ has equation $y=2x$. They meet at the origin $O$ and at the point $P$.
   Find the area of the finite region bounded by $C$ and $l$.2 marks
3. The curve $C$ has equation $y=x^3-6x^2+8x$.
   Show that $C$ crosses the $x$-axis at $x=0$, $x=2$ and $x=4$, and find $\int y\,\mathrm{d}x$.3 marks