Who can give me a hint of how to calculate this integral,Thanks

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In summary, the conversation discusses the use of GNU Octave and PTC Mathcad Prime 3.0 to express and evaluate the curve given by the integral \int_{0}^{\frac{-a}{2}+\frac{\sqrt{392-{a}^{2}}}{2}} {y}^{2}\arcsin\left({\frac{a+y}{\sqrt{196-{y}^{2}}}}\right)\,dy. The software is used to find numerical solutions and there is no specific formula for the curve.
  • #1
zhaojx84
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View attachment 7756
\(\displaystyle \int_{0}^{\frac{-a}{2}+\frac{\sqrt{392-{a}^{2}}}{2}} {y}^{2}\arcsin\left({\frac{a+y}{\sqrt{196-{y}^{2}}}}\right)\,dy\)
 

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  • #2
I'm not seeing an explicit evaluation, but I found the numerical solutions fascinating:View attachment 7762
 

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  • #3
tkhunny said:
I'm not seeing an explicit evaluation, but I found the numerical solutions fascinating:

Thanks very much. Could you tell me which software did you use to express this curve? Is there a formula for this curve. Thanks again for your help.
 
  • #4
zhaojx84 said:
Thanks very much. Could you tell me which software did you use to express this curve? Is there a formula for this curve. Thanks again for your help.

Hi zhaojx84, welcome to MHB! (Wave)

In GNU Octave, the free version of MatLab, we can do:
Code:
f = @(a, y) y^2 * asin((a + y) / (sqrt(196 - y^2)));
g = @(a) quad(@(y) f(a, y), 0, (-a / 2 + (sqrt(392 - a^2)) / 2));
x = -11:0.2:14;
y = arrayfun(g, x);
plot(x, y);

In Octave Online, we can quickly see what it does.

View attachment 7768
 

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  • #5
zhaojx84 said:
Thanks very much. Could you tell me which software did you use to express this curve? Is there a formula for this curve. Thanks again for your help.
I used PTC Mathcad Prime 3.0

It required pretty much what you see. Just type in what you want. The algebraic interpretation is provided.
 

Related to Who can give me a hint of how to calculate this integral,Thanks

1. How do I calculate this integral?

There are several methods for calculating integrals, including substitution, integration by parts, and using trigonometric identities. It is best to start by identifying which method is most appropriate for the integral in question.

2. Can you give me a hint for calculating this integral?

Unfortunately, without knowing the specific integral in question, it is difficult to provide a hint or guidance. It is important to understand the properties and rules of integrals in order to effectively solve them.

3. What should I do if I am stuck on an integral?

If you are stuck on an integral, it is helpful to review the basic rules and properties of integrals. It may also be beneficial to seek help from a tutor, classmate, or online resources.

4. How can I improve my skills in calculating integrals?

Practice, practice, practice! The more you practice solving integrals, the more comfortable and proficient you will become. It is also helpful to review examples and work through problems with step-by-step solutions.

5. Are there any tricks or shortcuts for calculating integrals?

While there are some techniques that can make certain integrals easier to solve, there is no substitute for understanding the fundamentals of integration. It is important to have a strong foundation in order to effectively use any tricks or shortcuts.

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