Question

which Technique of integration works better for the integral .4pi*((y+18.2)/4)^2*(9-y)

Answer 1

I think the better method is to simplify your function, using the properties of the algebra of real numbers

Answer 2

As @Michele_Laino said, this simplifies down into a nice simply polynomial:
\[4\pi(\frac{ y+18.2 }{ 4 })^2(9-y)\]
\[\pi\frac{(y+18.2)^2}{4}(9-y)\]
\[\frac{\pi}{4}(y^2+36.4y+331.24)(9-y)\]
\[\frac{\pi}{4}(-y^3-27.4y^2-3.64y+2981.16)\]
\[-0.25y^3\pi-6.85y^2\pi-0.91y\pi+745.29\pi \]

Integrating this, we get:
\[\int\limits-0.25y^3\pi-6.85y^2\pi-0.91y\pi+745.29\pi dy\]

You should be able to do the last bit :)

Answer 3

it was actually a 0.4pi but this explanation is very good. thank you

Answer 4

Oh sorry, I didn't see that. Fortunately it doesn't matter too much and as I suspect you already know, all you have to do is divide all of the terms in the integral by 10.

Answer 5

\[\int 0.4\pi \left(\frac{y+18.2}{4}\right)^2 (9-y)dy\] or rather \[ 0.4\pi\int \left(\frac{y+18.2}{4}\right)^2(9-y)dy\]

Answer 6

just wanted to write out the proper integral, tis all.

Answer 7

you could also try \( u = \dfrac{y+18.2}{4}\) so that \(\mathrm{d}y = 4\mathrm{d}u\)

Answer 8

but then how would you substitute in for \(9-y\)?

Answer 9

she is right.

Answer 10

ganeshie is right. the easiest thing to do is deal with the squared expression

Answer 11

u = ( y + 18.4) /4
du = 1/4 * dx

and by algebra

4u - 18.4 = y

therefore

9 - y = 9 - (4u - 18.4) = 27.4 - 4u