Can any one explain me about Integrals and derivatives in breif

In summary, the conversation discussed the topics of integrals and derivatives, with a recommendation for a helpful online resource and a brief explanation of their purposes. It also acknowledged the complexity of these concepts and the limitations of discussing them in a forum setting.
  • #1
srikar97
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Homework Statement



can anyone explain me about Integrals and derivatives in brief

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The Attempt at a Solution

 
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  • #2
A good reference to understand graphically what is happening can be found here http://hyperphysics.phy-astr.gsu.edu/hbase/math/derint.html" .
 
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  • #3
srikar97 said:

Homework Statement



can anyone explain me about Integrals and derivatives in brief
You seem to be asking for the equivalent of several university level lecture courses. Sadly, this is impossible in a forum setting such as this. You might try searching for some relevant lecture notes on the internet, in particular, MIT's site is extremely useful: http://ocw.mit.edu/index.htm
 
  • #4
srikar97 said:
can anyone explain me about Integrals and derivatives in brief

I'll try. You know that an equation can be plotted on a set of x-y axes. Well, the derivative of that equation at any value of x tells you the slope of that graph at that value of x (so this saves you having to draw the graph and trying to work out the approximate slope that way).

The integral of that equation between any two values of x tells you the area between the graph and the x-axis, and bounded by those two x values. This saves you having to draw the graph and trying to work out the approximate area, perhaps by counting squares and fractions of squares.

This is just a start, of course. Calculus can do much more.
 
  • #5
thank you all for the help!
 

Related to Can any one explain me about Integrals and derivatives in breif

1. What are integrals and derivatives?

Integrals and derivatives are mathematical concepts that are used to calculate the rate of change of a function. Derivatives are used to find the rate of change at a specific point on a curve, while integrals are used to calculate the total change over a given interval.

2. How are integrals and derivatives related?

Integrals and derivatives are inverse operations of each other. This means that if we take the derivative of a function, we can find its integral by reversing the process. This relationship is known as the Fundamental Theorem of Calculus.

3. What is the purpose of using integrals and derivatives?

Integrals and derivatives are widely used in various fields of science, engineering, economics, and finance to model and analyze real-world phenomena. They are also essential in solving optimization problems and finding the maximum or minimum values of a function.

4. How do you calculate integrals and derivatives?

To calculate derivatives, we use the rules of differentiation, such as the Power Rule, Product Rule, and Quotient Rule. Integrals can be calculated using techniques such as substitution, integration by parts, and partial fractions. We also use tables of integrals and derivatives to simplify the process.

5. What are some real-life applications of integrals and derivatives?

Integrals and derivatives have numerous applications in daily life, such as in calculating the speed and acceleration of an object, finding the area under a curve, predicting population growth, and analyzing financial data. They are also used in designing bridges, predicting weather patterns, and developing medical treatments.

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