Are integrals important in our society?

Answer

Integrals and derivatives are inextricably linked and are among the most important mathematical concepts. They are actually used in all fields of science and technology.
You probably know the most important formula of mechanics: F = ma
What is that a? That’s the acceleration vector, and the acceleration is the 2nd derivative of the place. To determine that position vector you will encounter integrals in one way or another. The above formula is an example of what is called a differential equation, so every time you use Newton’s law you will be dealing with derivatives and integrals. Integrals also occur in fluid mechanics, thermodynamics, electromagnetism, quantum mechanics, vibration analysis, astrophysics,… and indeed strength theory as used in architecture.
For example, another area where integrals are crucial is statistics. With continuous probability distributions such as the well-known normal distribution, you need an integral to calculate a probability.
What is also based on derivatives and integrals is Fourier analysis. Considering your age, I don’t think you’ve come across this yet, although you use it every day : Everyday applications such as JPG and MP3 are based on it.
But also mathematical models in biochemistry, for example, make use of these concepts.
You see, integrals and derivatives are everywhere. That is why they are also included in the curriculum of secondary school mathematics education. Precisely because they are so widely applicable.