Question

pls give me right ans x^2+4x^3 the is be y^3 how xd​

Answer 1

Step-by-step explanation:

I understand rotating about y=3 means it is a horizontal shift, and it is just like rotating about the x-axis except at y=3. Therefore, we will need to write,

x−y=1

in terms of x, which comes out out to:

y=x−1

B) I know the points of intersection between these 2 functions are at x=1, and x=4. so when writing the volume:

V=∫41π(outer−radius)2−(inner−radius)2dx

C) Because we have to rotate about y=3, we find the radius by subtracting the functions from 3 and determine which function is the outer and innder radius with respect to the line y=3.

The inner function would be y=x-1

3−(x−1)

which gives,

y=4−x

and the outer function

3−(x2−4x+3)

gives

4x−x2

So our volume then becomes,

V=π∫41(4x−x2)2−(4−x)2dx

Is this correct? After integrating I got 735π/5 which can be simplified with 147π. However, the answer key says 108π/5... I must have made an error somewhere.