# Definite integral with some unknown variables

• Mathematica
shinobi20
TL;DR Summary
I am evaluating a definite integral with unknown variables in Mathematica.
I am trying to evaluate an integral with unknown variables ##a, b, c## in Mathematica, but I am not sure why it takes so long for it to give an output, so I just decided to cancel the running. The integral is given by,

##\int_0^1 dy \frac{ y^2 (1 - b^3 y^3)^{1/2} }{ (1 - a^4 c^2 y^4)^{1/2} }##

Depending on the values of ##a, b, c## you can expect singularities in the integrand that may make the integral improper or even non-convergent. So, if the problem allows it, you should probably tell the software explicitly about assumptions on ##a, b, c##.

For example, I would begin by defining ##d := a^4 c^2## and passing the assumption that ##d < 1##.

Last edited:
• Dale
shinobi20
Depending on the values of a,b,c you can expect singularities in the integrand that may make the integral improper or even non-convergent. So, if the problem allows it, you should probably tell the software explicitly about assumptions on a,b,c.

For example, I would begin by defining d:=a4c2 and passing the assumption that d<1.
This is my code

Code:
d=2;
z=1;
b=a/z;
h=c^2 a^2d;
Integrate[ ( y^d (1 - (b y)^(d+1))^1/2 )/(1 - h^2d y^2d)^1/2 , {y,0,1}, Assumptions -> {y>0, h<1} ]

It does not return anything.