My Math Forum

My Math Forum (
-   Calculus (
-   -   Changing the intergrator (

Robertoo June 19th, 2014 02:41 PM

Changing the intergrator
Hi there,

I am studying for an exam, but I'm having problems with an integral, which is:

1/2 * integral(0 to pi)(y sin y^2) dy = 1/4 * integral(0 to pi)(sin y^2) dy^2

I have had some material on Riemann-Stieltjes integrals, which I can apply here, but I should not be using that for this course, as it is a more introductory course. I am curious if there are simple rules to change the integrator.

Thanks in advance.

v8archie June 19th, 2014 05:09 PM

Write $x = y^2$ then $\d{x} = 2y \d{y}$, $y = 0 \implies x=0$ and $y= \pi \implies x=\pi^2$
And wee thus have$$2 \int \limits_{0}^{\pi}y \sin{y^2} \d{y} = \int \limits_{0}^{\pi^2} \sin{x} \d{x}$$
which has an odd upper limit, but otherwise all is well.

All times are GMT -8. The time now is 07:04 AM.

Copyright © 2019 My Math Forum. All rights reserved.