# Integration (Related to Physics)

• _Mayday_
In summary, the conversation discusses using the general equation for a straight line to determine the gradient and the process of differentiating the equation to get to the gradient. However, there is some confusion about the correct formula for the gradient and the differentiation process. The conversation ends with a clarification on the thread title.
_Mayday_
[SOLVED] Integration (Related to Physics)

This shouldn't take long

I have been given the general equation for a straight line which is:

$$y=mx+c$$

Now I know that to determine the gradient I can use:

$$m=\frac{y}{x}$$

Here is my question. Can I differentiate the initial equation given to get to $$m=\frac{y}{x}$$

If so, which I am sure you can, then I seem to have come across a problem, though I think it is a problem in my differentiation.

$$y=mx=c$$

$$\frac{dy}{dx}=mx^{-1}$$

$$m=\frac{y}{x^{-1}}$$

or

$$m=\frac{x}{y}$$

This does not agree with my initial statement. Either my differentiation is incorrect or I need to touch up on my laws of indices, and if neither of these maybe I am deluded and this can't be done anyway

_Mayday_

(1) The slope is given by $m = \Delta y / \Delta x$, not $m = y/x$.
(2) The derivative (with respect to x) of mx + c is just m.

Doc Al said:
(1) The slope is given by $m = \Delta y / \Delta x$, not $m = y/x$.
(2) The derivative (with respect to x) of mx + c is just m.

Just noticed the thread title is integration not differentiation. Thank you for your help.

## 1. What is integration in physics?

Integration in physics is the process of finding the total value of a function over a certain interval. It is used to calculate quantities such as displacement, velocity, and acceleration, which are important in understanding the motion of objects.

## 2. What is the difference between integration and differentiation?

Integration and differentiation are inverse operations. While differentiation finds the rate of change of a function, integration finds the total value of a function. In other words, differentiation is used to find the slope of a curve, while integration finds the area under the curve.

## 3. Why is integration important in physics?

Integration is important in physics because it allows us to calculate important quantities such as displacement, velocity, and acceleration. These quantities are crucial in understanding the motion of objects and can help us make predictions about their future behavior.

## 4. What are the different types of integration?

The two main types of integration are definite and indefinite. Definite integration calculates the value of a function over a specific interval, while indefinite integration finds the general form of the function without any specific limits. Other types of integration include numerical integration (using numerical methods to approximate the integral) and line integration (calculating the integral of a function along a curve).

## 5. How is integration used in real-life applications?

Integration has a wide range of real-life applications, including in engineering, economics, and physics. For example, engineers use integration to calculate the work done by a force and the amount of energy needed to move an object. Economists use integration to study the relationship between supply and demand. In physics, integration is used to calculate the total distance traveled by an object and the total work done on an object by a force.

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