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Evaluate the definite integrals.$$\int_{2}^{3} \frac{d x}{x^{2}-1}$$

Calculus 2 / BC

Chapter 7

Integrals

Section 9

Evaluation of Definite Integrals by Substitution

Integration Techniques

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Lectures

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In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

27:53

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

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Evaluate the definite inte…

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Evaluate the integrals…

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Evaluate the given integra…

but the number 11 in the we need to evaluate the definite integral from what is it? From 2 to 3 D. X by X squared minus one. From 2 to 3 dx by access square minus one less class tickets. Yes so we'll be using a formula which is one by access choir minds. A Squire. Okay. From A to B. If it is so this becomes from it would be that's where minus a squared one by two. A Love model of X minus a by explore state. Okay similarly we will be using this formula from A. To be that is 2 to 3 and this is access square minus one. So one by two A. H one Love x minus a X minus one by express. When? Okay now will be start plugging in the parliament first so when bite will be taken as common upper limiting log three minus 12 by three minus lower limit log to minus when. So sorry to buy. It will be four for this Log one by three. Okay so this will be one by two which means one by two log one minus log too minus log one minus sorry plus log three. So one by two. This this will become equal to zero. Both are zero, so no the tree minus lot two. Okay, so this will be one by two, logs three by two, one by two, log three by two. So they should be the correct answer. Thank you so much.

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