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

[Rob K]

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

 

[JHamm]

$$\int^1_0y^8dy$$
Isn't quite $y^9|^1_0$

 

[Rob K]

hmm, I'm a little lost, I thought 1 to the power of anything will be 1 and so I get the same answer?

 

[Mark44]

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.

I tried this:

(5∏/2) [y⁸] with 1 at top 0 at bottom

You're missing an important step - finding the antiderivative of y⁸.

(5∏/2) [1] = 7.854.

What am I missing please?

Regards

Rob K

$$\int^1_0y^8dy$$
Isn't quite $y^9|^1_0$

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

 

[yenchin]

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?

 

[Rob K]

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

 

[JHamm]

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