# Three Problem Plus from Stewart Calculus

1. Jul 4, 2009

### yupenn

Three "Problem Plus" from Stewart Calculus

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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!!!

2. Jul 4, 2009

### Bohrok

Re: Three "Problem Plus" from Stewart Calculus

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

3. Jul 4, 2009

### yupenn

Re: Three "Problem Plus" from Stewart Calculus

4. Jul 4, 2009

### Bohrok

Re: Three "Problem Plus" from Stewart Calculus

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.

5. Jul 4, 2009

### VeeEight

Re: Three "Problem Plus" from Stewart Calculus

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

6. Jul 4, 2009

### yupenn

Re: Three "Problem Plus" from Stewart Calculus

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7. Jul 5, 2009

### HallsofIvy

Staff Emeritus
Re: Three "Problem Plus" from Stewart Calculus

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.