Thread: integration probem

I'm having problems figuring this out...

why does

INTa to b [y(x^2y')']dx = INTa to b [(yx^2y')'] - INa to b [x^2(y')^2]dx

Thank you!

Note: INTa to b just means "integral fom a to b"

Originally Posted by romtik

I'm having problems figuring this out...

why does

INTa to b [y(x^2y')']dx = INTa to b [(yx^2y')'] - INa to b [x^2(y')^2]dx

Thank you!

Note: INTa to b just means "integral fom a to b"

$\displaystyle \int_{a}^{b} yx^{2y}\,dx = \int_{a}^{b} yx^{2y} \, dx - \int_{a}^{b} x^2y^2 \, dx$ does not make sense. What do the ' represent?

Originally Posted by romtik

I'm having problems figuring this out...

why does

INTa to b [y(x^2y')']dx = INTa to b [(yx^2y')'] - INa to b [x^2(y')^2]dx

Thank you!

Note: INTa to b just means "integral fom a to b"

I cant tell but are you trying to do a method of integration by parts where $\displaystyle \int_a^{b}y(x^2y')'dx=\int_a^{b}y(x^2\frac{dy^2}{d ^2x}+2x\frac{dy}{dx})dx$?