Definite Integration: $$\int^{\frac{\sqrt{5}+1}{2}}_{1}$$

MHB
Thread starter juantheron
Start date Oct 14, 2016
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Integration

In summary, definite integration is a mathematical process used to find the exact value of an integral between two specified values, known as the limits of integration. It is different from indefinite integration, as it involves finding the numerical value of the integral rather than the antiderivative. The lower limit of integration is usually denoted as "a" and the upper limit as "b" due to mathematical convention. The definite integral is significant in real-world applications as it is used to find the area under a curve, with various uses in fields such as physics, engineering, and economics. There are different methods for evaluating definite integrals, depending on the complexity of the integral.

Oct 14, 2016

juantheron

Evaluation of $$\int^{\frac{\sqrt{5}+1}{2}}_{1}\frac{x^2+1}{x^4-x^2+1}\ln\left(x-\frac{1}{x}+1\right)dx$$

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Oct 14, 2016

alyafey22

Gold Member

MHB

What methods are expected to use ? what have you tried so far ?

Related to Definite Integration: $$\int^{\frac{\sqrt{5}+1}{2}}_{1}$$

1. What is definite integration?

Definite integration is a mathematical process used to find the exact value of an integral between two specified values, known as the limits of integration.

2. How is definite integration different from indefinite integration?

Definite integration involves finding the numerical value of an integral, while indefinite integration involves finding the antiderivative or general solution of the integral.

3. Why is the lower limit of integration usually denoted as "a" and the upper limit as "b"?

This is simply a convention in mathematics, where the variable "x" is typically used for the independent variable and "a" and "b" are used to represent the limits of integration.

4. What is the significance of the definite integral in real-world applications?

The definite integral is used to find the area under a curve, which has a wide range of applications in fields such as physics, engineering, and economics.

5. How can the definite integral be evaluated?

There are several methods for evaluating definite integrals, such as the fundamental theorem of calculus, u-substitution, and integration by parts. The most appropriate method depends on the complexity of the integral.