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

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Homework Help Overview

The discussion revolves around a trigonometric integral related to fluid mechanics, specifically within the context of flat plate boundary layer research. The integral in question is ∫sin(∏y/2δ)dy, evaluated over the interval from 0 to δ.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the evaluation of the integral and suggest possible methods of integration. Questions are raised regarding the specific method used to arrive at a proposed answer, and there is a suggestion of a substitution that may simplify the process.

Discussion Status

The discussion is active, with participants exploring different approaches to the integral. Some guidance has been offered regarding potential methods, but there is no explicit consensus on the best approach yet.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information available or the methods that can be employed. The specific setup of the integral and its boundaries are also under scrutiny.

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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