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

What these 12 flashcards ask

Area between y=f(x) and y=g(x) where f\ge g?
How do you find the limits for the area between two curves?
What if the curves cross again inside the interval?
Intersection of y=x^2-5x+6 and y=4-x^2?
Area between those two curves?
Area under a parametric curve?
What limits do you use for a parametric area integral?
Area under x=t^2, y=3t for 0\le t\le2?
Integration as a limit of a sum?
What does \delta x represent in \sum f(x)\,\delta x?
Left-hand rectangles under an increasing curve give?
Identity used for \int\cos^2t\,dt?

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

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
A curve $C$ has parametric equations $x=t^2$ , $y=3t$ , for $t\ge0$ .
Find the area described in part (b).2 marks
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).