Question

see attached... both questions

Answer 1

OK, the first question

Answer 2

Are you familiar with integrals?

Answer 3

yes

Answer 4

Cool, so to me, seems that the first question boils down to being an integral question for the function \[x^{1/2}\] on the interval [a,b]

Answer 5

ok. where did you get x^1/2?

Answer 6

In the question, you have \[\sqrt{x}\] which is \[x^{1/2}\]

Answer 7

Using the exponential form makes it easier to work with

Answer 8

oh, sorry, I was looking at a totally different problem just now! haha ok I totally see where you're coming from now

Answer 9

visually

Answer 10

Heh, right, no problem

Answer 11

The first equation actually is \[\[\int\limits_{a}^{b}x^{1/2}dx\]

Answer 12

What parts aren't you understanding?

Answer 13

I just don't know where all those numbers are coming frm before the sigma part. Is it a Reimann sum?

Answer 14

Yep, I think you're right

Answer 15

You can use the integral concept here because as \[n \rightarrow \infty\], the width \[\] gets infinitely small, and the subintervals become just the right size. if you can imagine before with the concept, if you were to try to approximate the area under the curve with just two subintervals, like 2 rectangles, the approximation would not be as good as one with 3 because they would fit a little better

Answer 16

Here is a nice picture

Answer 17

ok...

Answer 18

You had the curve for \[\sqrt{x}\], and your trying to find the area under the curve, on the closed interval [a,b]

Answer 19

And the sigma equation is telling to add up all the area of the subintervals, and the area of each subinterval is height * width...height is actually determined by the function \[\sqrt{x}\], like when you draw the graph of \[y=\sqrt{x}\], and then have the width ad \[\Delta x\]

Answer 20

The limit part before the sigma wants to consider as the width of each interval gets smaller and smaller, approaching so small that is difficult to determine, infinitely small, as \[n \rightarrow \infty\], so the space between each gets smaller and smaller

Answer 21

\[\int\limits_{a}^{b}x^{1/2}dx\]

Answer 22

So your limit + sigma equation has become the conventional representation of an integral I believe

Answer 23

ok. thank you. I have to go but thanks for your help and time!

Answer 24

Sure, I hope you can get at least the first question

Answer 25

Yes What they are trying to convey is riemanns sum

Answer 26

So I would first intewgrate x to the 1/2 and then plug in the b and a?

Answer 27

Yes, you'd do F(b) - F(a), where F(x) is the antiderivative found from integrating \[x^{1/2}\]