Is This the Correct Setup for a Double Integral to Find Area Between Curves?

In summary, the conversation is discussing finding the area of the region between the curves y=x3 and x=y2 in the xy-plane with given bounds for x and y. There is a question about whether to use a double integral or not, and a suggestion to draw a graph of the region. There is also a question about the wording of the problem and the possibility of not needing double integrals to find the area. The difficulty lies in determining the limits of integration.
  • #1
franky2727
132
0
simple question, for "find the area of the region between the xy-plane between the curves y=x3
and x=y2 where 0<x<1 , 0<y<1

is this the double integral for x3*y2 dy dx or for the double ingeral between x3+y2 dy dx?? i assume the first one? clarification needed please, can do the rest of the question :-)
 
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  • #2
franky2727 said:
simple question, for "find the area of the region between the xy-plane between the curves y=x3
and x=y2 where 0<x<1 , 0<y<1

is this the double integral for x3*y2 dy dx or for the double ingeral between x3+y2 dy dx?? i assume the first one? clarification needed please, can do the rest of the question :-)

Have you drawn a graph of the region? What you have above suggests to me that you haven't.

Are you sure this is the exact wording of the problem? Both of the curves you gave lie in the x-y plane. Might this be the problem?
find the area of the region **in** the xy-plane between the curves y=x3
and x=y2 where 0<x<1 , 0<y<1​

If so, you don't need double integrals to find this area.

On the other hand, if this is a problem where you're supposed to evaluate a double integral, the hard part is figuring out the limits of integration.
 

Related to Is This the Correct Setup for a Double Integral to Find Area Between Curves?

What is a double integral?

A double integral is a type of integration in which a function of two variables is integrated over a two-dimensional region in the xy-plane. This involves finding the area under the curve of the function in the given region.

What is the difference between a single integral and a double integral?

A single integral is used to find the area under a curve in one dimension, while a double integral is used to find the volume under a surface in two dimensions. Double integrals require two variables to be integrated, while single integrals only require one.

How is a double integral calculated?

A double integral is calculated by first determining the limits of integration for both variables, then setting up an iterated integral with one variable held constant while the other is integrated. This process is repeated until all variables have been integrated.

What are some real-life applications of double integrals?

Double integrals are commonly used in physics and engineering to calculate the volume of objects or the total mass of an object with varying density. They can also be used in economics to determine the total revenue or profit of a business over a given time period.

What are the types of double integrals?

There are two types of double integrals: Type I, which integrates over a rectangular region, and Type II, which integrates over a non-rectangular region. Type I integrals use the order of dx dy, while Type II integrals use the order of dy dx. The type of integral used depends on the given region and the function being integrated.

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