- #1
logicalman
- 22
- 0
Who can solve or give hint for the following integral?
[tex]\int_0^4 3x \sqrt{5^2-x^2}dx [/tex]
[tex]\int_0^4 3x \sqrt{5^2-x^2}dx [/tex]
Can You Tackle This Tricky Definite Integral Challenge?
- Thread starter logicalman
- Start date
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.
- #2
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
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Try a technique you learned in class!
- #3
mathlete
- 151
- 0
Try [tex]u=5^2-x^2[/tex], which means [tex]du = -2xdx[/tex]
- #4
logicalman
- 22
- 0
Thanks!
[tex]u^2=5^2-x^2[/tex] << This one works better.
[tex]u^2=5^2-x^2[/tex] << This one works better.
FAQ: Can You Tackle This Tricky Definite Integral Challenge?
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.
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.
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.
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.
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.