Volume Help (1 Viewer)

[goobi]

Question:

The region between y=x^2 and y=3x+4 is rotated about x=4. Find the volume formed. (Note that the region is not symmetrical about the y-axis.)

When I attempted this question using the cylindrical shell method, I wondered if I had to divide the region into two.

Also, it would be appreciated if anyone could help me solve it

Thanks!

 

[tomp1612]

v=pi*integral(dont know boundaries) of (4-x)(3x+4)(x^2) by cylindrical shells Im pretty sure thats the way to do it

 

[Carrotsticks]

What you can do, is shift the curve (and consequently the axes of rotation) such that instead of being at x=4, it is now x=0.

So you will need to map f(x) --> f(x+4) (this shifts it left by 4 units)

Now you can compute the volume as a normal 2U maths question.

 

[tomp1612]

What you can do, is shift the curve (and consequently the axes of rotation) such that instead of being at x=4, it is now x=0.

So you will need to map f(x) --> f(x+4) (this shifts it left by 4 units)

Now you can compute the volume as a normal 2U maths question.

ohh its x+4 new something was a bit weird

 

[goobi]

What you can do, is shift the curve (and consequently the axes of rotation) such that instead of being at x=4, it is now x=0.

So you will need to map f(x) --> f(x+4) (this shifts it left by 4 units)

Now you can compute the volume as a normal 2U maths question.

So what's the answer? Just double checking.

 

[tomp1612]

So what's the answer? Just double checking.

carrots way

 

[goobi]

Could someone please read over my solutions? Thanks.

 

[braintic]

Could someone please read over my solutions? Thanks.

View attachment 26500

Your solution looks fine except:
1. Its upside down!
2. You have made a small algebraic error in your expansion of the brackets
3. Even if correct, you would not get full marks. You are expected to show where your initial expression comes from, and not by quoting formulas. The simplest way is to show a typical cylindrical slice, and illustrate how it unwraps to form an approximate rectangular prism.