Substitution of variables to remove singularities.

[Mait]

Homework Statement

I am given an integral for which I need to substitute variables to remove a singularity so that the integral can be computed in Matlab using the Composite Trapezoidal Method, and then compared to the integral computed in Maple to 16 digit precision. I am stuck on the variable substitution. The integral is:

$\int_0^1 \frac{e^{-x}}{x^{3/4}}\,dx$

The Attempt at a Solution

I attempted the following substitution:
$du= \frac {dx}{x^{3/4}}$ so that $u=4x^{1/4}$ which resulted in the integral:
$\int_0^4 e^{ -{\frac{u^4}{256}}}\,du$

Which doesn't seem to work at all. I suspect the error is in the substitution of variables. Any help/input would be fantastic.

 

[Dick]

Homework Statement

I am given an integral for which I need to substitute variables to remove a singularity so that the integral can be computed in Matlab using the Composite Trapezoidal Method, and then compared to the integral computed in Maple to 16 digit precision. I am stuck on the variable substitution. The integral is:

$\int_0^1 \frac{e^{-x}}{x^{3/4}}\,dx$

The Attempt at a Solution

I attempted the following substitution:
$du= \frac {dx}{x^{3/4}}$ so that $u=4x^{1/4}$ which resulted in the integral:
$\int_0^1 e^ {\frac{u^4}{64}}\,du$

Which doesn't seem to work at all. I suspect the error is in the substitution of variables. Any help/input would be fantastic.

i) what happened to the minus sign in the exponential? ii) x isn't u^4/64. Check that '64'. And iii) when you go to the u integration, you'd better change the x limits to u limits.

 

[Mait]

Hey, the missing minus and 64 were typos. I changed x to equal u^4/256 and included the minus sign, and then changed the limits of integration from 0 to 1 to 0 to 4, but still no luck.

 

[Dick]

Hey, the missing minus and 64 were typos. I changed x to equal u^4/256 and included the minus sign, and then changed the limits of integration from 0 to 1 to 0 to 4, but still no luck.

Then it should be ok. How do you mean, 'no luck'?

 

[Mait]

The assignment said that removing the singularity would make it doable in Maple but all Maple is returning for me is a series of WhittakerM functions, which I am not familiar with. Perhaps the assignment made it seem to simple and more legwork is required.

 

[Mait]

Dick, the remaining issue was in my coding in Maple. Thank you very much for your help, it was great.