- #1

SolCon

- 33

- 1

Okay, I have 2 simple questions about integration. They are summarized in topic title.

1) This is the figure:

http://usera.ImageCave.com/biosyn/qq.PNG

It shows a curve y=x^2 and the line y=3+2x.

Point A is (3,9) and point B is (-1,1).

We have to calculate the area of the region enclosed between the curve and the line segment AB.

I have used the formula A=[tex]\int[/tex] (y2-y1) dx. Correct me if the formula is wrong. I've used the limits 3 and -1. Now, I have solved this and obtained the answer, but the problem is that the Area I'm getting is coming in negative. The answer to this question is 32/3 which is what I'm getting but only that it is -32/3.

Is this something to do with the figure or have I done something wrong?

2) This is the second part of a question. First part is done. We were asked to show the Volume, V cm^3, was given by:

V=12[tex]\pi[/tex]r

^{2}-2[tex]\pi[/tex]r

^{3}.

Okay, now the second part of the question says that Given that r varies, find the stationary value of V.

What I did here is, because the stat.value says that dV/dx = 0, I used:

0(dV/dx)=12[tex]\pi[/tex]r

^{2}-2[tex]\pi[/tex]r

^{3}.

0=24[tex]\pi[/tex]r-6[tex]\pi[/tex]r

^{2}.

After this, I don't know what else to do. The answer is coming as 64[tex]\pi[/tex]. But how is this coming?

Any help? :