Area between curves and integration as the limit of a sumEdexcel A-Level Maths: Mind map

Exam questions on Area between curves and integration as the limit of a sum

1. The curves $C_1$ and $C_2$ have equations $y=x^2-5x+6$ and $y=4-x^2$ respectively. They intersect at two points.
   Find the area of the region enclosed between the two curves.2 marks
2. A curve $C$ has parametric equations $x=t^2$, $y=3t$, for $t\ge0$.
   Find the area described in part (b).2 marks
3. The area under the curve $y=x^2$ for $0\le x\le3$ is being investigated using rectangles of equal width.
   Three rectangles of width $1$ are drawn, each with height equal to the value of $y$ at the left-hand end of its strip. Calculate their total area, and state with a reason whether it is an underestimate or an overestimate of the area under the curve.3 marks