Can You Solve This Challenging Definite Integral?

Thread starter logicalman
Start date Oct 31, 2004
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Definite integral Integral

In summary, a definite integral is a mathematical concept used to calculate the area under a curve on a graph within a specific interval. It is different from an indefinite integral in that it has specific limits of integration and gives a numerical value. The purpose of using a definite integral is to find important calculations in various fields. It is calculated using the fundamental theorem of calculus and has real-life applications in fields such as physics, engineering, economics, and statistics.

Oct 31, 2004

logicalman

Who can solve or give hint for the following integral?

[tex]\int_0^4 3x \sqrt{5^2-x^2}dx [/tex] :tongue:

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Oct 31, 2004

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

Try a technique you learned in class!

Oct 31, 2004

mathlete

Try [tex]u=5^2-x^2[/tex], which means [tex]du = -2xdx[/tex]

Oct 31, 2004

logicalman

Thanks!

[tex]u^2=5^2-x^2[/tex] << This one works better. :tongue:

1. What is a definite integral?

A definite integral is a mathematical concept that represents the area under a curve on a graph. It is used to calculate the total value of a function within a specific interval.

2. How is a definite integral different from an indefinite integral?

A definite integral has specific limits of integration, or starting and ending points, while an indefinite integral does not. This means that a definite integral gives a numerical value, while an indefinite integral gives a function.

3. What is the purpose of using a definite integral?

A definite integral is used to calculate the total value of a function within a specific interval. It can also be used to find the area under a curve, the volume of a solid, and other important calculations in various fields of science and engineering.

4. How is a definite integral calculated?

A definite integral is calculated using the fundamental theorem of calculus, which involves finding the anti-derivative of a function and evaluating it at the limits of integration. This can be done using various methods such as the Riemann sum, trapezoidal rule, or Simpson's rule.

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

Definite integrals have numerous real-life applications in fields such as physics, engineering, economics, and statistics. For example, they can be used to calculate the work done by a force, determine the velocity and acceleration of an object, and find the average value of a data set.