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realism877
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Homework Statement
(2(x)^2)/((x+1)((x)^2+1)) from 0 to 1
The indefinite answer is (1/2)ln2+ln2-(pi/4)
How did it get to this answer?(3/2)ln2-(pi/4)
LCKurtz said:Use partial fractions to write the integrand as
[tex]\frac A {x+1}+\frac{Bx+C}{x^2+1}[/tex]
What do you mean the indefinite answer? Where are the x's?realism877 said:The indefinite answer is (1/2)ln2+ln2-(pi/4)
A definite integral is a mathematical concept used to calculate the area under a curve on a given interval. It represents the accumulation of an infinitely large number of infinitesimal rectangles under the curve.
To calculate a definite integral, you need to use a specific formula or method, such as the Riemann sum, the Trapezoidal rule, or the Simpson's rule. These methods involve dividing the interval into smaller subintervals and approximating the area under the curve using geometric shapes.
A definite integral has specific values for both the upper and lower limits of integration, while an indefinite integral does not. In other words, a definite integral gives a numeric value, while an indefinite integral gives a function.
Definite integrals are used in various fields such as physics, engineering, economics, and statistics. For example, they can be used to calculate the work done by a force, the displacement of an object, or the average value of a function.
Some common challenges when calculating definite integrals include determining the correct method to use, dealing with complex functions, and finding the limits of integration. Additionally, numerical approximation methods may introduce errors in the final result.