# Calculus: Moments-Are these correct ?

• MitsuShai
In summary, the conversation involved calculating the moments Mx and My and the centroid of a lamina with density 15, which is in the shape of the region bounded by y=-x^2+1 and y=-3. The speaker had difficulty with the calculations but eventually got the values for My and xbar. They also attempted to calculate ybar and Mx, but kept making mistakes. They asked for confirmation on the values they got for ybar and Mx and mentioned they had trouble with the calculations due to constantly making mistakes.
MitsuShai
1. Calculate the moments Mx and My and the centroid of the lamina with density 15 that is in the shape of the region bounded by y=-x^2+1 and y=-3

I got the My and xbar. However, I keep messing up when doing the ybar and the Mx; I messed up like 5 times (no laughing). This time I got:
ybar: 24
Mx= 256

are these right?

I would show my work but that's A LOT of typing and the work on my paper is really really messing because I kept messing up. I know it's basically just plugging in numbers to the formula, but I mess up at every and any little thing.

nevermind.

## 1. What is calculus and why is it important?

Calculus is a branch of mathematics that deals with the study of change and motion. It is important because it provides a powerful set of tools for analyzing complex systems and solving problems in various fields such as physics, engineering, economics, and more.

## 2. What are moments in calculus?

Moments in calculus refer to the calculation of the center of mass or centroid of an object. It involves finding the average position of the object, taking into account the distribution of its mass.

## 3. What is the difference between first and second moments in calculus?

The first moment, also known as the centroid, is the average position of an object. The second moment, also known as the moment of inertia, is a measure of an object's resistance to rotational motion. It takes into account not only the average position but also the distribution of mass around that position.

## 4. How are moments used in real-life applications?

Moments are used in a variety of real-life applications, such as determining the stability of structures, analyzing the distribution of weight in a bridge or building, and calculating the center of gravity in a vehicle. They are also used in physics to study rotational motion and in economics to analyze supply and demand curves.

## 5. Is calculus necessary for understanding moments?

Yes, calculus is necessary for understanding moments as it provides the mathematical framework for calculating and analyzing them. Additionally, calculus concepts such as integration and differentiation are used in moments calculations to find the area and slopes of curves, respectively.

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