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

In summary, the integral is $$ \int_{-1}^1 \int_{-5}^{10} x^4 y dx~dy$$ and the final answer is 20625.
  • #1
jaydnul
558
15
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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  • #2
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?
 
  • #3
I see. 0. thanks
 
  • #4
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.
 
  • #5
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:
$$ \int_{-1}^1 \int_{-5}^{10} x^4 y dx~dy$$
 
  • #6
Oh ok good to know. Thanks guys!
 

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

1. What is a double integral?

A double integral is a mathematical concept used in calculus to calculate the area under a surface in a two-dimensional space. It involves calculating the sum of infinitesimal rectangles within a given region.

2. How is a double integral different from a single integral?

A single integral is used to calculate the area under a curve in one dimension, while a double integral is used to calculate the area under a surface in two dimensions. Double integrals require an additional integration step and can be thought of as a combination of two single integrals.

3. What is the purpose of solving a double integral problem?

Solving a double integral problem allows us to calculate the area under a two-dimensional surface, which has many real-world applications. It is also a fundamental concept in multivariable calculus and is used to calculate volumes, masses, and moments of inertia.

4. What are the steps for solving a double integral problem?

The first step is to set up the limits of integration for both variables, which define the region of integration. Then, the integrand (function being integrated) is multiplied by an infinitesimal area element. The integral is then evaluated using appropriate integration techniques, such as substitution or integration by parts.

5. What are some common mistakes when solving a double integral problem?

Some common mistakes include incorrectly setting up the limits of integration, forgetting to include the area element, and making errors during the integration step. It is also important to carefully consider the order of integration to ensure the correct result is obtained.

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