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

In summary, a trigonometric integral is an integral that involves trigonometric functions and is used to solve problems related to curves and angles in mathematics and physics. To solve a trigonometric integral, techniques such as substitution, integration by parts, and trigonometric identities can be used. The purpose of using trigonometric integrals is to solve problems involving curves and angles in various fields of science and engineering. There are specific rules for solving trigonometric integrals, including the power rule, product rule, quotient rule, and chain rule. While software and calculators can be used to solve these integrals, it is still important to have a good understanding of the concepts and techniques involved.
  • #1
Victor2167
2
0
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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  • #2
What about -2δ/∏ cos(∏y/2δ) from 0<y<δ ?

Which evaluates to: -2δ/∏( cos(∏/2) - 1) = 2δ/∏
 
  • #3
what method of integration is used to obtain that answer?
 
  • #4
Is the integral you are doing
[tex] \int_{0}^{\delta} \sin\left( \frac{\pi y}{2 \delta} \right) dy [/tex]
?

There is an obvious choice of substitution to do
 

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

What is a trigonometric integral?

A trigonometric integral is an integral that involves trigonometric functions such as sine, cosine, and tangent. It is used to solve problems related to curves and angles in mathematics and physics.

How do I solve a trigonometric integral?

To solve a trigonometric integral, you can use techniques such as substitution, integration by parts, or trigonometric identities. It is important to have a good understanding of trigonometric functions and their derivatives to solve these types of integrals.

What is the purpose of using trigonometric integrals?

Trigonometric integrals are used to solve problems involving curves and angles, such as finding the area under a curve or calculating the displacement of a particle. They are also used in various fields of science and engineering, including physics, astronomy, and mechanics.

Are there any specific rules for solving trigonometric integrals?

Yes, there are specific rules that can be used to solve different types of trigonometric integrals. These include the power rule, product rule, quotient rule, and chain rule. It is important to understand these rules and how to apply them correctly in order to solve trigonometric integrals.

Can trigonometric integrals be solved using software or calculators?

Yes, there are many software programs and calculators that can solve trigonometric integrals. However, it is still important to have a good understanding of the concepts and techniques involved in solving these integrals, as software and calculators may not always give accurate or complete solutions.

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