Integrating 3x^3: Simplifying the Process

Thread starter dan greig
Start date Apr 24, 2006
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Integration

In summary, integration is a mathematical process used to find the area under a curve or the accumulation of a quantity over a certain interval. It is important in various fields of science, such as physics, engineering, and economics, as it allows for accurate calculations of quantities like displacement, velocity, and work. There are several methods of integration, including the fundamental theorem of calculus, substitution, integration by parts, and partial fractions. Integration and differentiation are inverse operations, and integration is used in many real-world applications, such as thermodynamics, determining the center of mass, and predicting population growth.

Apr 24, 2006

dan greig

how do i integrate,

3x^3

is it left as

3x^4/4

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Apr 24, 2006

Homework Helper

Correct, don't forget the constant of integration though

Apr 24, 2006

neutrino

If it's an indefinite integral, you have to add a constant.

Apr 24, 2006

dan greig

you mean +c?

Apr 24, 2006

Jacobpm64

yep.. that +c is important.. and many teachers will be ready and willing to dock many points off for that

What is integration?

Integration is a mathematical process that involves finding the area under a curve or the accumulation of a quantity over a certain interval.

Why is integration important?

Integration is important in many fields of science, including physics, engineering, and economics. It allows us to accurately calculate quantities such as displacement, velocity, and work.

What are the different methods of integration?

There are several methods of integration, including the fundamental theorem of calculus, substitution, integration by parts, and partial fractions. Each method is useful in different situations and can make the integration process easier.

How is integration related to differentiation?

Integration and differentiation are inverse operations. This means that if we integrate a function, we can then differentiate the resulting function to get back to the original function.

What are some real-world applications of integration?

Integration is used in many real-world applications, such as calculating the area under a pressure curve to determine the work done in a thermodynamic process, finding the center of mass of an object, and predicting population growth in biology.