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

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The discussion revolves around solving the definite integral (5∏/2) ∫y^8 dy from 0 to 1, which equals 0.873. The user, Rob, initially misunderstands the integration process and incorrectly calculates the integral without finding the correct antiderivative. The correct antiderivative of y^8 is y^9/9, and the evaluation at the limits 0 and 1 is crucial for obtaining the final result. Rob expresses a struggle with integration compared to differentiation and seeks a deeper understanding of the concepts involved. The conversation highlights the importance of grasping the fundamentals of integration to succeed in mathematical applications, especially in engineering.
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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\int^1_0y^8dy
Isn't quite y^9|^1_0
 
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:
\frac{5\pi}{2}\int_0^1 y^8~dy
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:
\int^1_0y^8dy
Isn't quite y^9|^1_0

That's wrong, too. The antiderivative of y8 is \frac{y^9}{9}
 
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 \frac{y^9}{9}

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