1. ## Numerical Integration

Find the surface area given

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

I need a step by step solution using numerical integration.

The chapter in the book is very unclear to me.

2. ## Re: 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?

3. ## Re: Numerical Integration

Am I correct in assuming you are rotating around the x axis?

4. ## Re: Numerical Integration

What I am looking for is the area of surface of revolution using numerical integration.

5. ## Re: Numerical Integration

Originally Posted by HallsofIvy
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?
What I am looking for is the area of surface of revolution using numerical integration.

6. ## Re: Numerical Integration

Originally Posted by Prove It
Am I correct in assuming you are rotating around the x axis?
What I am looking for is the area of surface of revolution using numerical integration.

7. ## Re: Numerical Integration

Originally Posted by nycmath
What I am looking for is the area of surface of revolution using 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?

8. ## Re: Numerical Integration

Originally Posted by Plato
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?
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.

9. ## Re: Numerical Integration

Originally Posted by Plato
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?
He means integration using numerical methods.

10. ## Re: Numerical Integration

Originally Posted by Prove It
He means integration using numerical methods.
That is a meaningless statement. All integrals are numbers. So all integration is numerical.

11. ## Re: 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?

12. ## Re: Numerical Integration

I have not learned this topic. I skipped over the chapter because it is not easy to grasp.

13. ## Re: Numerical Integration

Originally Posted by nycmath
I have not learned this topic. I skipped over the chapter because it is not easy to grasp.
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.