Area between a curve and a line or two curvesEdexcel International A Level Maths: Mind map

Exam questions on Area between a curve and a line or two curves

1. The line $y=2x$ meets the curve $y=6x-x^2$ at the origin $O$ and at the point $A$.
   Find the area of the finite region bounded by the line and the curve.2 marks
2. The curve $y=x^2$ and the line $y=x+2$ intersect at the points $P$ and $Q$.
   Find the area of the region bounded by the curve $y=x^2$, the $x$-axis and the lines $x=-1$ and $x=2$.2 marks
3. The curve $C$ has equation $y=x^2-4x+5$ and the line $l$ has equation $y=x+1$.
   Find the coordinates of the points where $l$ meets $C$.3 marks