Area between curvesAQA A-Level Maths: Flashcards

What these 12 flashcards ask

Area between y=f(x) and y=g(x) for a\le x\le b with f\ge g?
How do you find the limits of the enclosed region?
How do you tell which graph is the upper one?
Why must you not divide by x when solving x^2=2x?
What does \inta^b f(x)\,dx give when the curve is below the x-axis?
What goes wrong if the curves cross between the limits?
Area between y=x^2 and y=2x?
\int{-1}^{2}(2+x-x^2)\,dx?
The area between a curve and a line can be found another way. How?
If you get a negative area, what has probably happened?
Area enclosed by y=x and y=x^3?
Should answers be exact or decimal?

Exam questions on Area between curves

The curve $C$ has equation $y=x^2$ and the line $L$ has equation $y=2x$ .
Find the exact area of the region enclosed by $C$ and $L$ .2 marks
The curve $C$ has equation $y=x^2+1$ and the line $L$ has equation $y=x+3$ .
Find the area of the region enclosed by $C$ and $L$ .2 marks
The curve $C$ has equation $y=x^3$ and the line $L$ has equation $y=x$ .
Find the $x$ -coordinates of the three points where $C$ and $L$ intersect.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).