Find the surface area given

y = cuberoot(x) + 2 from [1,8].

I need a step by step solution using numerical integration.

I know nothing about this method.

The chapter in the book is very unclear to me.

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- Apr 28th 2014, 07:57 AMnycmathNumerical Integration
Find the surface area given

y = cuberoot(x) + 2 from [1,8].

I need a step by step solution using numerical integration.

I know nothing about this method.

The chapter in the book is very unclear to me. - Apr 28th 2014, 08:39 AMHallsofIvyRe: Numerical Integration
This is not very well phrased! "Surface area" usually refers to a three dimensional figure, not a figure in the xy-plane. But if you are just talking about the area in the xy- plane, you have not defined a

**closed**region. Are x= 1, x= 8, and y= 0 also boundaries? Or are you talking about the area of the figure formed when this graph is rotated about the x-axis? - Apr 28th 2014, 08:43 AMProve ItRe: Numerical Integration
Am I correct in assuming you are rotating around the x axis?

- Apr 28th 2014, 09:10 AMnycmathRe: Numerical Integration
What I am looking for is the area of surface of revolution using numerical integration.

- Apr 28th 2014, 03:41 PMnycmathRe: Numerical Integration
- Apr 28th 2014, 03:42 PMnycmathRe: Numerical Integration
- Apr 28th 2014, 03:59 PMPlatoRe: Numerical Integration
I have followed this thread just to see what developed.

I know that I am old and have not been active in integration studies in fifteen years, but I did do a PhD thesis in this area.

That said, I have absolutely no idea what you could possibly mean by "".*numerical integration*

What do you mean? - Apr 28th 2014, 04:23 PMnycmathRe: Numerical Integration
Numerical Integration is a chapter title in my single variable calculus book. The three authors concluded that there are functions that simply cannot be solved using basic integration formulas. I will provide more detail from the textbook chapter on this topic tomorrow.

- Apr 28th 2014, 06:52 PMProve ItRe: Numerical Integration
- Apr 29th 2014, 06:06 AMPlatoRe: Numerical Integration
- Apr 29th 2014, 08:27 AMHallsofIvyRe: Numerical Integration
You repeatedly said "What I am looking for is the area of surface of revolution" but did not say what the axis of revolution was! Is it correct that the curve is rotated around the

**x- axis**?

Also, there are a number of ways to do "numerical integration"- rectangles, trapezoid rule, and Simpson's rule are most popular. Which have you learned? - Apr 29th 2014, 02:54 PMnycmathRe: Numerical Integration
I have not learned this topic. I skipped over the chapter because it is not easy to grasp.

- Apr 29th 2014, 03:19 PMPlatoRe: Numerical Integration
I was afraid of that. You may not realize that entire textbooks (indeed, graduate texts) have been devoted to this topic in numerical analysis.

**How do you expect us to know what methods you have available if you, yourself have skipped over the material?**

Go back to Prof. Ivy's reply. Read it. Then review the textbook to see which on his list are discussed in your text.