Iterated integrals help, See attached,

I understand that the iterated integral is measuring area under the function in the x or y direction. I just don't see how to determine the line from this picture. I feel like its painfully obvious, but even looking though the section in my book I'm not getting it.

Question

Iterated integrals help, See attached,

I understand that the iterated integral is measuring area under the function in the x or y direction. I just don't see how to determine the line from this picture. I feel like its painfully obvious, but even looking though the section in my book I'm not getting it.

anonymous · Answer

attachment

anonymous · Answer

I know that being the inside integral can be a function of x, so i think c should be something like, 1/2x

anonymous · Answer

Find the slope.

anonymous · Answer

$$
y-y_0 = \frac{y_1-y_0}{x_1-x_0}(x-x_0)
$$

anonymous · Answer

do I offset it with anything? Like a shift of the graph since it doesnt go throgh 0,0?

anonymous · Answer

$$
(x_0,y_0) = (3,0),\quad (x_1,y_1) = (5,1)
$$

anonymous · Answer

Solve for $y$, go go go .

anonymous · Answer

y=1/2x-3/2

anonymous · Answer

Don't forget your parenthesis man.

anonymous · Answer

i get (y-0)=1/2(x-3)

anonymous · Answer

Sure.

anonymous · Answer

i dont distribute the 1/2 through the parenthesis?

so its just y=1/2x-3?

anonymous · Answer

or are you just saying to write them to clean it up, so y=(1/2)x-(3/2)?

anonymous · Answer

Never write 1/2x

anonymous · Answer

Either do 1/(2x) or (1/2)x or x/2  depending on what you mean.

anonymous · Answer

Got it, thanks for the help

amistre64 · Answer

|dw:1362358369347:dw|

anonymous · Answer

Ah, I like that amistre, thats a good way to think about these, I should start labeling

amistre64 · Answer

pictures always help me out with these things :)