Three Problem Plus from Stewart Calculus

[yupenn]

Three "Problem Plus" from Stewart Calculus

Homework Statement

Please visit Google Book for online access to the Stewart Calculus 6ed.
http://books.google.com/books?id=EBE3vMmGu50C&pg=PP1&dq=stewart+calculus&ei=gYdPSvXyB4_AlQTg9PCACw

The problem No. 3,4 and 8 that are located on Page 380 and 381.

Homework Equations

The Attempt at a Solution

for prob 3: it's hard to work out two points of intersection since the equation is cubic.
for prob 4: i don't figure out how to choose the "direction" of cross-sections.
for prob 8: we need to calculate the volume of the overlap section. but how?
Thanks!

 

[Bohrok]

There's no preview available for the book...

 

[yupenn]

There's no preview available for the book...

please follow my link. it may take some time to download the image of preview.

 

[Bohrok]

When I click the link, some gray text on the page says "No preview available"
Previews of Google books always load immediately for me, but nothing loads for this one because there is no preview, at least for me in Firefox and IE.

 

[VeeEight]

I'm also getting a "No preview available" message - perhaps you should post the questions

 

[yupenn]

thanks. I've uploaded the screenshot.

 

[HallsofIvy]

Problem 3 says:
The figure shows a horizontal line, y= c, intersecting y= 8x- 27x². (It might be x³- the screenshot is very small.) Find the number c such that the areas of the shaded regions are equal. The first shaded region is outside the parabola and below the line y= c. The second is the region above the line and below the parabola.

Using vertical rectangles and Letting x₀ and x]sub]1[/sub] be the x values where the parabola and rectangle intersect, the first integral is
$$\int_0^{x_0} [c- (8x- 27x^2)] dx$$
and the second is
$$\int_{x_0}^{x_1} [8x- 27x^2- c] dx$$
Do those integrals, set them equal and solve for c. Here, the hard part is finding x₀ and x₁.