How Do You Solve the Trigonometric Integral in Fluid Mechanics Research?

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SUMMARY

The integral ∫sin(∏y/2δ)dy for 0 PREREQUISITES

  • Understanding of trigonometric integrals
  • Familiarity with substitution methods in calculus
  • Knowledge of fluid mechanics principles, particularly boundary layer theory
  • Proficiency in evaluating definite integrals
NEXT STEPS
  • Study advanced techniques in integration, focusing on substitution methods
  • Explore fluid mechanics textbooks that cover boundary layer theory
  • Learn about numerical methods for evaluating complex integrals
  • Investigate applications of trigonometric integrals in engineering problems
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Researchers in fluid mechanics, engineering students, and professionals working on boundary layer analysis who require a deeper understanding of trigonometric integrals and their applications.

Victor2167
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Working on some fluid mechanics research for flat plate boundary layer, stuck on this integral:

∫sin(∏y/2δ)dy for 0<y<δ

Any help would be deeply appreciated.
 
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What about -2δ/∏ cos(∏y/2δ) from 0<y<δ ?

Which evaluates to: -2δ/∏( cos(∏/2) - 1) = 2δ/∏
 
what method of integration is used to obtain that answer?
 
Is the integral you are doing
\int_{0}^{\delta} \sin\left( \frac{\pi y}{2 \delta} \right) dy
?

There is an obvious choice of substitution to do
 

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