Struggling to Evaluate This Double Integral?

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Discussion Overview

The discussion revolves around evaluating a double integral of the form double integral (e^(y^3)) dy dx, with specific limits for dy from sqrt(x/3) to 1 and dx from 0 to 3. Participants express their struggles with the integration process, particularly with the integration of e^(y^3).

Discussion Character

  • Homework-related

Main Points Raised

  • One participant expresses confusion about how to start evaluating the double integral.
  • Another participant explains that double integrals can be treated like normal integrals by treating the other variable as a constant during integration.
  • A participant notes that the integration of e^(y^3) is challenging and does not provide a straightforward solution.
  • There is mention of the possibility of integrating with respect to x first, but the participant still finds the resulting integral difficult.
  • One participant shares the correct LaTeX representation of the integral but admits to limited understanding of the problem.
  • A later reply indicates that one participant has resolved their confusion, though the specifics of their solution are not detailed.

Areas of Agreement / Disagreement

Participants generally agree on the difficulty of the integral, particularly the integration of e^(y^3). However, there is no consensus on the best approach to evaluate the integral, and some participants express uncertainty about the integration process.

Contextual Notes

Participants do not provide specific methods for integrating e^(y^3), and there are unresolved questions about the steps involved in evaluating the double integral.

Who May Find This Useful

Students or individuals seeking assistance with double integrals, particularly those struggling with integration techniques involving exponential functions.

ChargedTaco
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Evaluate.

double integral (e^(y^3)) dy dx

Where dy is evaluated from sqrt(x/3) to 1

...and dx is evaluated from 0 to 3.

I am lost.
I don't even know how to start.:frown:
 
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do u know how to do integrals?
double integral is just normal integrals in disguise, so when ou are doing the "y"-integral, you treat all "x"s in the integrand as just a constant, and while doing the "x"-integral you treat all "y"s as constant. Then, everything would then be exactly the same as a normal single integral. In many cases, whether you do the x or y integral first does not matter.
in your case i think you should do y first
 
The "y" integration doesn't look pretty. It's basically

\int_{a}^{b} e^{y^3}{}dy
 
Hey guys yes I do know how to do integrals...however I don't know how to do this one. If I integrate y first I have to integrate e^(y^3)dy...and i don't know how to do this.

If I integrate x first then I'll end up with having to
integrate 3e^(y^3)dy...and I again I don't know how to do this.

Thanks.
 
Here it is.

\int_{0}^{3} \int_{sqrt(x/3)}^{1} e^{y^3} {}dy} {}dx

Yay! I got the latex code...however this is the only thing I know about this problem.
 
Last edited:
Nevermind...I got it. Thanks guys.
 

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