Porisma

A hint to get started

Read a selected region before splitting rotation disks

The diagram shows y2=6−xy^2=6-x and y=−xy=-x.

(i) State their intersection coordinates.

(ii) Find the exact area of the finite region between the two graphs.

(iii) The shaded region RR is bounded by the y-axis, the line and the lower part of the parabola. Find the volume when RR rotates through 2π2\pi about the y-axis, to 2 decimal places.

Expand diagram

Use the scrollbars or arrow keys to inspect details.

Parabola x=6−y² and line x=−y intersect at (−3,3) and (2,−2). R is shaded between the y-axis and the nearer positive-x boundary, from y=−sqrt(6) to zero; it changes boundary at (2,−2).
Parabola x=6−y² and line x=−y intersect at (−3,3) and (2,−2). R is shaded between the y-axis and the nearer positive-x boundary, from y=−sqrt(6) to zero; it changes boundary at (2,−2).
Parabola x=6−y² and line x=−y intersect at (−3,3) and (2,−2). R is shaded between the y-axis and the nearer positive-x boundary, from y=−sqrt(6) to zero; it changes boundary at (2,−2).

[2008/RJC/Promo/9(modified)]

CJC · Review problems · Question 12

Use y as the integration variable and read which boundary is nearer the axis at each height.

Read the worked solution