Sunday

November 23, 2014

November 23, 2014

Posted by **Taeyeon** on Sunday, March 11, 2012 at 2:34pm.

a. Set up but do not evaluate an integral representing the area of R. Express the integrand as a function of a single variable.

b. Set up but do not evaluate an integral representing the volume of the solid generated when R is rotated about the x-axis. Express the integrand as a function of a single variable.

c. Set up but do not evaluate an integral representing the volume of the solid generated when R is rotated about the y-axis. Express the integrand as a function of a single variable.

- calculus -
**Steve**, Sunday, March 11, 2012 at 7:22pmFirst, see where the curves intersect. Just substitute y=9-3x into the equation for the ellipse to find they intersect at (0,9) and (3,0)

So, the integrals will all be for x in [0,33 or y in [0,9]

(a) ∫[0,3] y1-y2 dx

= ∫(9-3x) - sqrt(9-3x^2) dx

(b) volume using discs is

∫pi*(R^2-r^2) dx

where R = 9-3x and r=sqrt(9-3x^2)

= pi∫(9-3x)^2 - (9-3x^2) dx

(c) same idea, different axis

pi∫(3 - y/3)^2 - (3 - y^2/3) dy

**Answer this Question**

**Related Questions**

calculus - 2. Let R be the region in the first quadrant bounded by the graphs of...

Calculus - Use the shell method to set up, but do not evaluate, an integral ...

calculus - 1. Find the area of the region bounded by f(x)=x^2 +6x+9 and g(x)=5(x...

calculus - 2. Sketch the region in the first quadrant that is bounded by the ...

Calculus AB/AP - Use the rectangles with the given dimensions to approximate the...

calculus - 1. Let S be the region in the first quadrant bounded by the graphs of...

Calculus AB - Let R be the region bounded by the graphs of y=sin(pi x) and y=(x^...

calculus - using the method of shells, set up, but dont evaluate the integral, ...

Calculus AP - Let R be the region in the first quadrant bounded by the graph y=3...

calculus - Let R be the region in the first quadrant bounded by the graphs of y=...