Integration over a Region in the First Quadrant without a Prefix.

In summary, the set up for the given problem is to integrate e^slnt over the region in the first quadrant of the st-plane, above the curve s=lnt, from t=1 to t=2. The correct set up for this problem would be to start with an integral from t=1 to t=2 and then integrate from s=ln1 to s=ln2. It is important to consider the limits of s at each value of t or vice versa.
  • #1
s7b
26
0
Hi,

I was just wondering if the set up for this problem; integrate f(s,t)=e^slnt over the region in the first quadrant of the st-plane that lies above the curve s=lnt from t=1 to t=2

is:

integral(t=1 to t=2)integral(s=ln1 to s=ln2) of e^slnt

If that's not the right set up what am I doing wrong
 
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  • #2
Hi s7b! :smile:

(have an integral: ∫ :wink:)
s7b said:
integral(t=1 to t=2)integral(s=ln1 to s=ln2) of e^slnt

No … you can either start ∫(t=1 to t=2), or start ∫(s=ln1 to s=ln2) …

but then you have to ask what are the limits of s at each value of t (or vice versa) :smile:
 

What is a double integral?

A double integral is a mathematical concept used to calculate the volume under a two-dimensional surface in three-dimensional space. It is an extension of the concept of a single integral, which is used to calculate the area under a curve.

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

A single integral is used to calculate the area under a curve, while a double integral is used to calculate the volume under a two-dimensional surface. Additionally, while a single integral has only one variable, a double integral has two variables, typically represented by x and y.

What are the applications of double integrals?

Double integrals have a wide range of applications in mathematics, physics, and engineering. They are used to calculate volumes, surface areas, moments of inertia, and center of mass for various shapes and objects. They are also used in vector calculus for calculating flux, work, and circulation.

How do you solve a double integral?

To solve a double integral, you first need to set up the limits of integration for both variables, typically x and y. This involves determining the boundaries of the region over which the integral is being evaluated. Then, you can use various integration techniques, such as the Fubini's theorem, to evaluate the integral.

What is the significance of the order of integration in a double integral?

The order of integration in a double integral refers to the order in which the two variables, typically x and y, are integrated. This can affect the complexity of the integral and the ease of evaluation. Choosing the appropriate order of integration can make the integral easier to solve and can also provide insight into the problem being studied.

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