Help on integration of this problem

h0kashi0

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Hello, I just need some slight help on how to go about the integration of this problem in terms of x as I cant seem to find out how to integrate e^x^5. Thank you
 

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Dr.Peterson

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Hello, I just need some slight help on how to go about the integration of this problem in terms of x as I cant seem to find out how to integrate e^x^5. Thank you
This is a definite integral. You will not be able to find the antiderivative you are looking for, and must use other methods.

What course is this for? What techniques have you been learning?
 

h0kashi0

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this is or an engineering course at university. We have been doing double integrals and just integrating the terms inside normally, no specific techniques. I just don't know how to go about actually integrating it in terms of x if you know any techniques?
 

Cubist

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I guess it would it be OK, in this context, to assume that x and y are independent variables?

[math] I = \int_0^1 {\int_{y^4}^1 y^{15} e^{x^5} dx}\, dy[/math]
 

Dr.Peterson

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this is or an engineering course at university. We have been doing double integrals and just integrating the terms inside normally, no specific techniques. I just don't know how to go about actually integrating it in terms of x if you know any techniques?
Here is how I know you couldn't find the indefinite integral without special techniques:


1636030237535.png
1636030292709.png
 

Cubist

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Here is how I know you couldn't find the indefinite integral without special techniques:

I just tried changing the order of integration and I think the integral becomes much nicer.

@h0kashi0 have you learnt about this technique? If so then I'd start with a sketch of the relevant x,y region which helps to get the new limits correct.
 
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h0kashi0

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I attempted to swap the order of integration and found the boundaries that I wrote down. But when integrating with respect to y, it came back with the e^x^5 term and i can't seem to integrate it again with respect to x. Is it okay to see if the boundaries I worked out were wrong?
 

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h0kashi0

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Actually sorry, i rearranged the x=y^4 wrong that's why my answer was wrong. I've got it now and i managed to integrate with respect to x as well. Thank you for the help
 
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