Wednesday

August 27, 2014

August 27, 2014

Posted by **Leona** on Sunday, February 27, 2011 at 6:38pm.

y=x^3, x=y^3; rotated about x-axis

I first made y=x^1/3, then x^3=x^1/3

Then I tried to do an integration from 0 to 1 with x^1/3-x^3, but I can't get one of the possible answers, which are:

A. 16/35π

B. 16/7π

C. 18/35

D. 7/2

E. 16π

Any advice?

- Calculus -
**Helper**, Sunday, February 27, 2011 at 7:52pm| = integrate symbol

y = x^3

y^3 = x, y = x^(1/3)

Using the formula

pi | (f(x))^2 - (g(x))^2 dx

pi | (x^3)^2 - x^(1/3)^2 dx

pi | (x^6) - x^(2/3) dx

pi ( 1/7 x^7 - 3/5 x^(5/3))

When I evaluated from 0 to 1,

I got,

- 16/35 pi

- Calculus -
**Helper**, Sunday, February 27, 2011 at 8:03pmCorrection for above,

| = integrate symbol

y = x^3

y^3 = x, y = x^(1/3)

Using the formula

pi | (f(x))^2 - (g(x))^2 dx

pi | x^(1/3)^2 - (x^3)^2 dx

pi | x^(2/3) - (x^6) dx

pi ( 3/5 x^(5/3) - 1/7 x^7 )

When I evaluated from 0 to 1,

I got,

16/35 pi

**Related Questions**

Calculus - Let R be the region bounded by y=6sin((pi/2)x), y=6(x-2)^2, y=3x+3 ...

Calculus - Determine the volume of the solid abtained when the region bounded by...

please help calculus - find the volume of the solid formed by revolving the ...

Calculus - *Note I reposted this question as I changed the subject** The Region...

calculus - The region bounded by the curve y=1÷(1+2x) , the line X=2 , the x-...

Calculus - Let R be the square region bounded by y = 2, x = 2, and the x and y-...

Calc - The region bounded by y=2.5x^2 and y=4x is to be rotated about both axes ...

First Moment - The Region "R" under the graph of y = x^3 from x=0 to x=2 is ...

Calculus AB...I really need help - The region in the first quadrant enclosed by ...

AP Calculus - Let R be the first quadrant region enclosed by the graph of y= 2e...