Finding the Volume of a solid by integration

[calcstudent04]

I need help with these 2 problems.

problem 1:
Find the volume if the solid obtained when the region bounded by the x-axis, the y-axis, and the line y-x=3 is rotated about the x-axis.

problem 2:
The regionbounded by the graph of f(x)=x^2+1 and the x-axis between x=0 and x=2 is rotted about the y-axis. Find the volume of the resulting soild

 

[NateTG]

Have you covered solids of rotation in class?

 

[calcstudent04]

yes. Have you?

 

[Chen]

Then you should know that if you revolve the area under the graph of f(x) for $$a \geq x \leq b$$ about the X axis, the volume is given by:
$$V = \pi \int _a^b f(x)^2dx$$

 

[calcstudent04]

I worked the problem using that formula I just need to know if you got the same. For the first one I got 9pi and on the secong I got14pi

 

[calcstudent04]

I really would appreciate any help

 

[jon]

I got 6pi for the second one using cylindrical shells method

height of each cylinder is y = x^2 + 1

radius of each cylinder is simply "x"

circumference of each cylinder is 2pi times "x"

Then integrate over the interval [0,2]

 

[jon]

Sorry I meant to say second one is 12 pi

 

[HallsofIvy]

1. These should be posted in the "homework help" section.

2. You should show us what you have tried on homework problems.

3. In the original post you did NOT ask us to verify your answer and did not tell us what you got.

4. The first figure is a cone with base radius and height both equal to 3 and so has volume 9π.

5. The second problem can be done by "shells" as jon said and the volume is indeed 12π.