# Help Calculating Definite Integral

• realism877
In summary, the conversation is about finding the indefinite answer for the integral (2(x)^2)/((x+1)((x)^2+1)) from 0 to 1, which is equal to (1/2)ln2+ln2-(pi/4). The person asking the question is trying to understand how the answer was obtained, and the other person suggests using partial fractions to simplify the integrand. The initial confusion about the answer being an elementary algebra question is cleared up, and the conversation ends with the person asking for clarification on where the x's are in the answer.
realism877

## Homework Statement

(2(x)^2)/((x+1)((x)^2+1)) from 0 to 1

How did it get to this answer?(3/2)ln2-(pi/4)

Use partial fractions to write the integrand as
$$\frac A {x+1}+\frac{Bx+C}{x^2+1}$$

LCKurtz said:
Use partial fractions to write the integrand as
$$\frac A {x+1}+\frac{Bx+C}{x^2+1}$$

I did that.

I already have the solution. I'm just trying to figure out where the 3 came from.

Oh my! I thought you had a calculus question about integrating. Instead you have an elementary algebra question. See if you can figure out how to combine like terms and make your answer agree with the given answer.

realism877 said:
What do you mean the indefinite answer? Where are the x's?

## What is a definite integral?

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.

## How do I calculate a definite integral?

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.

## What is the difference between a definite and indefinite integral?

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.

## What are some real-life applications of definite integrals?

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.

## What are some common challenges when calculating definite integrals?

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.

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