Integrating Functions with Only One Variable for Beginners

NihalRi
Messages
134
Reaction score
12
1. Homework Statement
image.jpg

I'm trying to integrate this, the only variable is y the others(x,w) are all constants.

Homework Equations


The ways of integrating that I am familiar with are substitution, trigonometric substitution, by parts & partial fraction decomposition.

The Attempt at a Solution


Looking at this I can't think of where I'd begin, should I rearange? Is it multistep? It it possible ? I'd appreciate any help :)
 
Physics news on Phys.org
NihalRi said:
1. Homework Statement
View attachment 108595
I'm trying to integrate this, the only variable is y the others(x,w) are all constants.

Homework Equations


The ways of integrating that I am familiar with are substitution, trigonometric substitution, by parts & partial fraction decomposition.

The Attempt at a Solution


Looking at this I can't think of where I'd begin, should I rearange? Is it multistep? It it possible ? I'd appreciate any help :)

PF rules say that you are required to put in effort and show your work. So, try out the methods you have learned. If Method I does not work, then try Method II. If that does not work, turn to Method III, etc. And yes, indeed, it takes some (possibly wasted) work and uses a lot of (possibly wasted) paper but that is how you will learn.
 
Last edited:
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
Back
Top