got a couple of questions finding the area (1 Viewer)

[red802]

1)the area of the region bounded by the curves y=x^2 and y=x+2 between x = 0 and x = 1 is rotated about the x axis. find the volue of the generated solid

2) find the area bounded by the curve y = √9 - √x and the x and y axis
find the volume of the solid generatetd when this area is rotated about:
i) the x axis
ii) the y axis

if u can show the working out because i cant figure them out

 

[Riviet]

1)the area of the region bounded by the curves y=x^2 and y=x+2 between x = 0 and x = 1 is rotated about the x axis. find the volue of the generated solid

This one is not hard, the curves cross at (1,3) so you can go straight to subtracting areas. So take the integral from 0 to 1 of x+2-x² since you subtract area under parabola from the area under the linear function.

 

[richz]

1) int from 0 to 1 (x+2-x^2)^2 dx
keep on going and i think the answer is 4.95pi

2) int from 0 to 3 (root9 - rootx) (im assuming its between 0 and 3)
and do all the tedious work. And u shud get the answer to b 9-2root3
i)same as 2 but ur squaring (root9 -rootx) then int
ii) i think u shud get the same answer as i

sorry if i get any of these rong, i havent done much maths since my last exam, so i'll b a bit rusty.