Definite Integration: Solve (5∏/2) ∫y8 dy = 0.873

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Discussion Overview

The discussion revolves around the process of definite integration, specifically evaluating the integral (5∏/2) ∫y^8 dy from 0 to 1, and understanding the steps involved in finding the antiderivative and applying the limits of integration.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • Rob K expresses confusion about the integration process and the missing steps in his textbook example.
  • Rob K attempts to evaluate the integral but arrives at a numerical result of 7.854, questioning what he is missing.
  • Another participant points out that the antiderivative of y^8 is not simply y^9, but rather y^9/9.
  • Rob K acknowledges the need to find the antiderivative and reflects on his struggles with integration compared to differentiation.
  • There is a discussion about the evaluation of the integral at the limits, with some participants clarifying the correct approach to applying the limits of integration.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct evaluation steps for the integral, as there are multiple interpretations of the antiderivative and the application of limits. Some participants challenge each other's claims without resolving the disagreements.

Contextual Notes

Rob K's confusion highlights potential gaps in understanding the fundamental concepts of integration, particularly the process of finding antiderivatives and applying limits. There are also indications of varying levels of comfort with mathematical concepts among participants.

Who May Find This Useful

This discussion may be useful for students learning about definite integration, particularly those who are struggling with the concepts of antiderivatives and the evaluation of integrals.

Rob K
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Hi, me again,

I'm struggling with definite integration, I have an example here in a book, but it has skipped the integration steps.

Can some one explain to me how

(5∏/2) ∫y8 dy = 0.873.

I don't know how to show the numbers at the top and bottom of the integration sign these numbers are 1 at the top and 0 at the bottom.

I tried this:

(5∏/2) [y8] with 1 at top 0 at bottom

(5∏/2) [1] = 7.854.

What am I missing please?

Regards

Rob K
 
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[tex]\int^1_0y^8dy[/tex]
Isn't quite [itex]y^9|^1_0[/itex]
 
hmm, I'm a little lost, I thought 1 to the power of anything will be 1 and so I get the same answer?
 
Rob K said:
Hi, me again,

I'm struggling with definite integration, I have an example here in a book, but it has skipped the integration steps.

Can some one explain to me how

(5∏/2) ∫y8 dy = 0.873.

I don't know how to show the numbers at the top and bottom of the integration sign these numbers are 1 at the top and 0 at the bottom.
Like this:
[tex]\frac{5\pi}{2}\int_0^1 y^8~dy[/tex]
If you right-click on this expression, there's an option to show the LaTeX code, so you can see how I did it.
Rob K said:
I tried this:

(5∏/2) [y8] with 1 at top 0 at bottom
You're missing an important step - finding the antiderivative of y8.
Rob K said:
(5∏/2) [1] = 7.854.

What am I missing please?

Regards

Rob K

JHamm said:
[tex]\int^1_0y^8dy[/tex]
Isn't quite [itex]y^9|^1_0[/itex]

That's wrong, too. The antiderivative of y8 is [itex]\frac{y^9}{9}[/itex]
 
Last edited:
Rob K said:
hmm, I'm a little lost, I thought 1 to the power of anything will be 1 and so I get the same answer?

Do you know how to perform the integration?
 
Yes yes yes, thank you, I understand now. I keep forgetting that with integration you increase the power by 1 and then divide by the new power.

Unfortunately my integration is not good which is strange, as I find and have always found Differentiation an absolute doddle. I need to find the intuition behind maths before I understand it, I can't parrot fashion to get by. Which is a problem when you are doing an Engineering degree...

Thanks for you help.

Rob
 
Mark44 said:
That's wrong, too. The antiderivative of y8 is [itex]\frac{y^9}{9}[/itex]

I know, that's why I said it wasn't quite y9
 

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