🍕 AN INTEGRAL APPLICATION | HARD LEVEL 🔥

PROPOSED PROBLEM:
Three math students will order a 36-centimeter pizza. Instead of fatiá-la in a traditional way, they decide to fatiá-la with parallel cuts, as shown in the figure. Being students of mathematics, they are able to determine where to eat so that each one eats the same amount of pizza. Onde foram feitos os cortes?
To solve this problem we are going to go through the calculation of the area below a curve (equação da circumferência) by integral, isso hair fat of each fatia ter must be the same amount of pizza, therefore, the same area.
To determine "c", which corresponds to the distance from the center of the pizza to where it must be made or cut, we must assemble an integral and apply the necessary integration techniques to be used in a function F(c), not which one must be applied Numerical methods or use of software to find the roots of F and assim, determine "c".
And how to mount integral for this problem?
We know f(x) (integrating) and the area (A) below the curve, but we do not know the upper limit of integration "c", which is or what we want, logo:
f(x) = √R² - x²
A = 𝜋R²/12
∫f(x)dx [0, c] = A, to be solved to integral applying the integration techniques, we obtain:
F(c) - A = 0
To find the zero of the function F, I used the Winplot software.
I hope you enjoyed the content by leaving it alone 👍 and sharing it with your friends who have difficulties in this matter. A strong hug and obrigado hair support forever!
TO ATTEND FOLLOW:
Solved exercise of INTEGRAÇÃO BY FRAÇÕES PARTIAIS 👇:
• CÁLCULO 1: INTEGRAIS |...
ABOUT OR CHANNEL:
The channel has the objective of contributing to the learning of students who study engineering, through the step-by-step resolution of exercises of disciplines taught in the graduation course.
VIDEO CHAPTERS:
00:00 Interpreting or Problem
03:30 Determining the Equação da Circumferência
05:10 A Area as a Definite Integral
06:50 Integration by Trigonometric Substitution
18:50 Applying the Fundamental Theorem of Calculus
21:40 Using the Winplot Program to Find the Zero da Função
📚 Exercise taken from: Calculus Volume 1 - 7th Ed. (James Stewart)
📸 INSTAGRAM: / engstevenroger

[@fernandomedeiros815]

Parabéns! Ótima explicação.

Muito obrigado, Fernando!

[@sullywhisonant6301]

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