Question

The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method.

Answer 1

y = −x^2 + 8x − 15, y = 0; about the x-axis
Our teacher prefers us to use shells. I don't know how to solve for X :/

Answer 2

factor

Answer 3

y = (-x +3)(x-5)

Answer 4

split it up
-x = -3
x = 5

Answer 5

(x = 3 or 5)

Answer 6

@iTz_Sid

Answer 7

its not 5 or 3.....

Answer 8

ok and

Answer 9

i tried it out it doesn't work

Answer 10

how so?

Answer 11

when you plug the numbers in, they check out

Answer 12

y = 0 if u put x = 3 or 5 the equation isn't 0

Answer 13

dont forget, it is - x^2

Answer 14

ok if it were x = - 5 it will end up - 30

Answer 15

but i said 3 and 5, not negative

Answer 16

i know but if u were to put the negative on the other side it would be x = -3 or -5 it means the same things as -x = 3 or 5

Answer 17

and u r correct it is -3 i only tried out -5 x = -3

Answer 18

or as u say it -x = 3

Answer 19

i said -x = -3

Answer 20

whatever, the answer is 3 and 5

Answer 21

there can't be two answers x can only be one number

Answer 22

I meant find the equation for X
As in X=.....

Answer 23

complete the square ??hmm

Answer 24

hmm thats a completely different game

Answer 25

@OtherWorldly all that arguing... for nothing

Answer 26

yup XD

Answer 27

i would use disk method easy pzy

Answer 28

You don't know how to solve for x?
Come on Sid :d get your head in the game!

Complete the square.\[\large\rm y=-(x^2-8x)-15\]Half of 8 is 4,
4 squared is 16,
so I guess that completes the square for us,\[\large\rm y=-(x^2-8x+16)-15+16\]Subtract 1 to the other side,\[\large\rm y-1=-(x^2-8x+16)\]Rewrite as perfect square, multiply by negative 1,\[\large\rm 1-y=(x-4)^2\]Square root,\[\large\rm \sqrt{1-y}=x-4\]Add 4,\[\large\rm 4+\sqrt{1-y}=x\]

Answer 29

Ooooooh. xD

Answer 30

Note that y = −x^2 + 8x − 15 has the graph of an inverted parabola. That is, the parabola opens down. You should find the x-coord. of the points where the graph intersects the x-axis. Draw the entire solid. Then it may become easier for you to visualize how you might use the shell method.

Answer 31

no luck.. i guess
we still have to write the function in terms of y for disk method
right ?

Answer 32

In terms of y for disks? :o
Hmm I don't think so.

I can see that my drawing was a little off hehe.
I just knew it was some kind of parabola opening downward XD