5.12 Areas and volumes of revolutionIB Maths: Applications and Interpretation HL: Flashcards

What these 13 flashcards ask

Area between y=f(x) and the x-axis for a\le x\le b, where f\ge0?
What does a negative value of \inta^b f(x)\,dx tell you?
How do you find the total area when a curve crosses the x-axis in the interval?
Why is \int0^6(x^2-4x)\,dx=0 not the area?
Formula for the area between a curve and the y-axis from y=c to y=d?
Volume when a region is rotated 360^\circ about the x-axis?
Volume when a region is rotated 360^\circ about the y-axis?
What is the radius of each disc for rotation about the x-axis?
For y=\sqrt{x}, what is y^2?
Volume of y=\sqrt{x}, 0\le x\le4, rotated about the x-axis?
For rotation about the y-axis, what must you do to the curve y=x^2 first?
Can a volume of revolution be negative?
What should you show in working when using the GDC for a volume?

Exam questions on 5.12 Areas and volumes of revolution

The curve $C$ has equation $y=x^2-4x$ .
Use your GDC to find the total area enclosed between $C$ and the $x$ -axis for $0\le x\le6$ .2 marks
For $k>0$ , the region $R_k$ is enclosed by the curve $y=\sqrt{x}$ , the $x$ -axis and the line $x=k$ . The region is rotated through $360^\circ$ about the $x$ -axis to form a solid of volume $V$ .
Find the value of $k$ for which $V=18\pi$ .2 marks
The curve $y=x^2$ is drawn for $x\ge0$ . Distances are in centimetres. The region $S$ is enclosed by the curve, the $y$ -axis and the line $y=9$ .
The region $S$ is rotated through $360^\circ$ about the $y$ -axis to model a bowl. Find the exact volume of the bowl.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).