Applications of Integrals

🔻Hello Guys!🔺

Firstly let me thank you for visiting this site.

I'm trying my best to share a little bit knowledge of application in the real world using Integral.
So I hope I didn't do any miss interpretation, and I hope by the end of this section you should barely understand about this concept can be applied in the real world.

1. Area between Curves 💢

2. Arc Length 💢

3. Surface Area of Revolution 💢

These are the applications I want to talk about today.

• Area between Curves👈

These are some formula that can be used for determining the area between curves. The formula isn't universal. So there are some condition that formula can be used or not.

a. If the area is between an graph (f(x)) and (above) x-axis

b. If the area is between a graph (f(x)) and (below) x-axis, therefore we put minus(-) in the formula.

c. Combination for determining the area between a graph (f(x)) and (above and below) x -axis.

d. If the area is between two graph ( f(x) and g(x) )

So, if you asked why we have to use integrals to determine the area, why we just don't calculate directly using the two-dimensional shape formula.

OK, you can use two-dimensional shape formula but you need to cut it into pieces and make sure that their shapes are similarly close with regularly shape (ex: rectangle,trapezium, square, circle,est). If that so, you will cost more time to spend on and your result can't be accurate.

source: http://nandawikyta.blogspot.co.id/2013/05/pengertian-terasering.html

•       Arc Length👈

            This is the formula to determine the arc length:

How do we apply this into the real world? Well, if you're an engineer and you have a project to build a bridge. You can use arc length formula to determine how long cables you will need to connect one tower onto another.

source: https://www.pinterest.com/cindytrepko/golden-gate/

•        Surface of Revolution👈

In this case you want to determine the area of things in real life which is 3-D, but what you have learned just in 2-D graph. We want to determine the area of surfaces.

Come from 2-D graphic turned into 3-D , by rotating them in x-axis or y-axis.

source: https://www.youtube.com/watch?v=EBfxiKQLnJ4

Here the formula for making you easier to keep on.

source: https://www.youtube.com/watch?v=EBfxiKQLnJ4

How do we apply this into the real life? if you' re an owner of interior industrial and you need to count the area that need to be painted, so you have to calculate those for having a minimum cost.

👉👉👉



source:http://loaf.com/products/mini-gaston-lamp-black

Okay, I think that's all I can share for now. Hope you can understand  and realize that integrals are very useful in daily life.

Thank you for your attention.

Have a good day! 👊💃