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

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SUMMARY

The discussion centers on setting up a double integral for the function f(s,t) = e^s * ln(t) over a specific region in the first quadrant of the st-plane, bounded by the curve s = ln(t) from t = 1 to t = 2. The correct setup for the integral is integral(t=1 to t=2) integral(s=ln(1) to s=ln(2)) of e^s * ln(t). Participants clarify that the order of integration can be switched, but it requires careful consideration of the limits of integration for each variable.

PREREQUISITES
  • Understanding of double integrals in calculus
  • Familiarity with the properties of exponential and logarithmic functions
  • Knowledge of the first quadrant in the Cartesian coordinate system
  • Ability to determine limits of integration based on region boundaries
NEXT STEPS
  • Study the concept of changing the order of integration in double integrals
  • Learn about the application of exponential functions in integration
  • Explore the use of logarithmic functions in calculus
  • Practice setting up double integrals over various regions in the Cartesian plane
USEFUL FOR

Students and educators in calculus, mathematicians working with integrals, and anyone interested in advanced integration techniques in multivariable calculus.

s7b
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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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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:
 

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