What is the solution to a double integral problem with given limits?

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Homework Help Overview

The discussion revolves around evaluating a double integral of the function x^4y with specified limits for x and y. Participants are attempting to understand the correct approach to solving this integral and are exploring potential errors in their calculations.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are sharing their attempts at evaluating the integral and questioning the accuracy of their evaluations. There is a focus on the correct setup of the integral and the evaluation process.

Discussion Status

Some participants have provided feedback on the attempts, indicating that there may be errors in the evaluation of the integrand. Multiple interpretations of the integral setup are being explored, and there is an ongoing exchange of clarifications regarding the notation for definite integrals.

Contextual Notes

Participants express uncertainty about how to format the integral correctly in the math code and are discussing the implications of their choices on the evaluation of the integral.

jaydnul
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Homework Statement
[tex]∫∫x^4ydxdy[/tex]
x [-5,10]
y [-1,1]
(don't know how to do a definite integral in the math code...)

The answer choices are
[itex]A)10^5[/itex]
[itex]B)0[/itex]
[itex]C)-10^{10}[/itex]

The attempt at a solution
[itex]\frac{x^5y}{5}[/itex] evaluated at -5 to 10.

then
[itex]∫20625ydy[/itex] evaluated at -1 to 1.

My final answer is 20625. What did I do wrong?
 
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Jd0g33 said:
Homework Statement
[tex]∫∫x^4ydxdy[/tex]
x [-5,10]
y [-1,1]
(don't know how to do a definite integral in the math code...)

The answer choices are
[itex]A)10^5[/itex]
[itex]B)0[/itex]
[itex]C)-10^{10}[/itex]

The attempt at a solution
[itex]\frac{x^5y}{5}[/itex] evaluated at -5 to 10.

then
[itex]∫20625ydy[/itex] evaluated at -1 to 1.
Your integral above is OK, but you fouled up when you evaluated the integrand. Try again.
Jd0g33 said:
My final answer is 20625. What did I do wrong?
 
I see. 0. thanks
 
Jd0g33 said:
Homework Statement
[tex]∫∫x^4ydxdy[/tex]
x [-5,10]
y [-1,1]
(don't know how to do a definite integral in the math code...)

The answer choices are
[itex]A)10^5[/itex]
[itex]B)0[/itex]
[itex]C)-10^{10}[/itex]

The attempt at a solution
[itex]\frac{x^5y}{5}[/itex] evaluated at -5 to 10.

then
[itex]∫20625ydy[/itex] evaluated at -1 to 1.

My final answer is 20625. What did I do wrong?

Just fyi, to do a definite integral it's \int_{#}^{#} the _{#} being the bottom number, ^{#} being the top number.
 
So the full integral would look like this:
Code:
$$ \int_{-1}^1 \int_{-5}^{10} x^4 y dx~dy$$

I put this inside HTML code tags so that you could see the script without the browser rendering it. In rendered form, it looks like this:
$$ \int_{-1}^1 \int_{-5}^{10} x^4 y dx~dy$$
 
Oh ok good to know. Thanks guys!
 

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