Math Help - Urgent!!! disk and washer method

1. Urgent!!! disk and washer method

I can't get these 4 problems. I just don't get how to do them. I had a sub today in math and my teacher had us learn the chapter ourselves and do it but i can't get these answers. Help w/ explaining would highly be appreciated!!! I don't care if you only do one or two, i just need to grasp the subject. 1. find the volume of the solid bounded by these equations about the indicated lines. equations: y=square root of (x) y=0 x=4. About the line x=6. 2. sames as above: equations y=2x^2 y=0 x=2 about the line y=8.

3. same above : y=6-x y=0 y=4 x=0 about the line x=6.
4. y=x * square root of (4-x^2) about y=0.

Please Hurry!!! thanks in advance and i will be waiting here trying to figure them out Thanks!!

2. ok

The fourth one is just a basic one you need to use the formula V=pi* $\int_a^{b}R(x)^2-r(x)^2dx\$...so you see that you need to find the zeros of $x(4-x^2)^{\frac{1}{2}}\$ so either x=0 or $(4-x^2)^{\frac{1}{2}}\$=0 so x=0 or x= $\pm$2 by graphing you will see that you need to set up two integrals since [-2,0] the graph is below the x-axis and from [0,2] its above so what you do is apply the formula v=pi* $\int_a^bR(x)^2-r(x)^2dx\$ so V in this case is equal to pi* $\int_{-2}^{0}0-x(4-x^2)^{\frac{1}{2}}dx\$+pi* $\int_0^{2}x(4-x^2)^{\frac{1}{2}}-0,dx\$=well I will leave that up to you

the other ones when you revolve it around a vertical axis I'd use shell method which is V=2 $pi\$ $\int_a^{b}h(x)g(x)dx\$ where h(x) is the the distance from the axis to any point in the region you are revolving and g(x) is your curve

3. thanks but for 4. shouldn't you square the equation. i got 128 pi /15 for that

4. Haha

Wow yes you aer right I suck so follow everything I said except it should now be $[x(4-x^2)^{\frac{1}{2}}]^2\$ in each integral..and that simplifies to $4x^2-x^4\$...which then integrates to $\frac{4}{3}x^3-\frac{1}{5}x^5\$..haha sorry about that lol

5. i don't get your other formula with h(x)g(x) i don't think we've learned that yet. What i did was move the equation over for example if it was square root of (x) and it said revolve around x=4 i'd add four so it moved the equation back 4 and then revolved around the y for the answer.

6. If you are going to do it

without the shell method you have to solve the equation so that it is no longer a function of x but now a function of y and use v=pi* $\int_c^d{R(y)^2}dy$

7. no i knew that but i was asking if there's an easier way

8. Ok

no there is not withou the shell method...occasionally there are little teensy short cuts such as $\int_{-a}^{a}f(x),dx$=2 $\int_0^{a}f(x).dx$ when f(x) is an even function but no...its really just that hard at your level...sorry

9. so my ways the only way ...so far?

10. yes

Unfortunately it is....you should learn an easier way...or Triple integrals ...jk...just sit tight and do it the long way...it will come eventually

11. alright thanks bud, i really appreciate it. Finally finished see ya

12. Hah

no problem...Im always here if you need help!o and good job for finishing