# MATH

posted by .

Compute the volume of the solid obtained by rotating the region in the first quadrant encolsed by the graphs of the functions y = x^2 and y = sqrt(x) about the y-axis.
I keep getting (1/3)pi and can't figure out what I'm doing wrong!

• MATH -

rotating about the y -axis needs
V = π∫x^2 dy

first equation:
y = x^2
2nd equation:
√x = y
x = y^2
x^2 = y^4

so V = π∫y dy - π∫y^4 dy
= π [ (1/2)y^2 - (1/5)y^5] from y = 0 to 1
= π( 1/2 - 1/5)
= (3/10)π

## Similar Questions

1. ### Calculus

1. Find the volume formed by rotating the region enclosed by x=5y and x=y^3 with y¡Ý0 about the y-axis. 2. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis y=18x-6x^2 …
2. ### Calculus

This problem set is ridiculously hard. I know how to find the volume of a solid (integrate using the limits of integration), but these questions seem more advanced than usual. Please help and thanks in advance! 1. Find the volume of …
3. ### Calculus AB

Consider the region trapped between the graphs of y=9-x^2 and y=11-3x. a) find the area of this region b) set up an integral which computes the volume of the solid of rotation obtained by rotating this region about the x-axis c) set …
4. ### Calculus AB

Consider the region bounded by the graphs of the equations x=y^2 and y=3x. Set up 2 integrals, one with respect to x and the other with respect to y, both of which compute the volume of the solid obtained by rotating this region about …
5. ### Calculus AB

Consider the region trapped between the graphs of y=9-x^2 and y=11-3x. a) find the area of this region b) set up an integral which computes the volume of the solid of rotation obtained by rotating this region about the x-axis c) set …
6. ### Calculus

a) Find the volume formed by rotating the region enclosed by x = 6y and y^3 = x with y greater than, equal to 0 about the y-axis. b) Find the volume of the solid obtained by rotating the region bounded by y = 4x^2, x = 1, and y = 0 …
7. ### Calculus I don't understand

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 10 x and y = 5 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded by y=8 x^2, x …
8. ### Calculus

Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g. A. The region R is the base of a solid. For this solid, the cross sections, …
9. ### Calculus

Find the volume of the solid obtained by rotating the region enclosed by the graphs of y=18-x, y=3x-6 and x=0 about the y-axis V=
10. ### Calculus

Hello, I would like to make sure the answers to these questions are correct. 1. Using the shell method, what is the volume of a solid that is generated by rotating the region by y = x^2 and x = y^2 about the x axis. My Work: r = y …

More Similar Questions