Rules for all calculations regarding integration

In summary, the conversation is about integration in a math course. The person is looking for help with understanding the necessary rules and applications for this concept. Another user has provided a link to an online tutorial that may be helpful and a third user has highlighted the importance of integration in various calculations and applications.
  • #1
pavadrin
156
0
Hey
I’ve now come across integration in my maths course for my first time. I was wondering if somebody out there might be able to help me with a couple issues regrading this topic. Firstly I would appreciate if I could be told all the necessary rules for all calculations regarding integration. If this list is too long and/or complicated then please only list the fundamentals for this concept. Secondly I would like to know about possibly applications for this integration concept.
Thank you greatly to those who reply,
Pavadrin
 
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  • #2
  • #3
Integration can be used to calculate volumes, centres of mass, moment of inertia, work done by a force, the displacement from velocity, velocity from acceleration, etc. It can also be used to find probabilities, arc lengths of curves, surface area of 3D shapes, shortest distance between two points on a surface, and many other places. So, integration is very, very important.
 
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  • #4
thanks for the link nazzard
 

Related to Rules for all calculations regarding integration

1. What is integration?

Integration is a mathematical process used to find the area under a curve. It is also known as anti-derivative because it is the inverse operation of differentiation. Integration is commonly used in physics, engineering, and other sciences to solve problems involving continuous quantities.

2. What are the basic rules for integration?

The basic rules for integration are the Power Rule, Constant Multiple Rule, Sum/Difference Rule, and the Rule of Integration by Parts. These rules help in solving integrals by simplifying the process and reducing it to a set of standard forms that can be easily solved.

3. How do you integrate trigonometric functions?

To integrate trigonometric functions, you need to use the appropriate trigonometric identities and substitution techniques. The most commonly used identities are the Pythagorean identities, double-angle identities, and half-angle identities. Substitution techniques involve substituting the trigonometric function with a variable and using the chain rule to solve the integral.

4. Can integration be used to find the volume of a solid?

Yes, integration can be used to find the volume of a solid. This is known as the method of cylindrical shells or the disk/washer method. It involves breaking down the solid into infinitely thin cylindrical shells or disks, calculating the volume of each shell or disk, and then integrating to find the total volume.

5. What is the difference between definite and indefinite integration?

Definite integration involves finding the exact value of an integral within a specific interval. It gives a numerical value as the result. On the other hand, indefinite integration involves finding the antiderivative of a function without specifying the bounds of the integral. It gives a general equation as the result.

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