Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Use the Comparison Theorem to determine whether the integral is convergent or divergent.

$ \displaystyle \int_1^\infty \frac{x + 1}{\sqrt{x^4 - x}}\ dx $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Diverges

02:45

Wen Zheng

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

Campbell University

University of Michigan - Ann Arbor

University of Nottingham

Boston College

Lectures

01:53

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.

03:49

Use the Comparison Theorem…

02:16

02:27

02:00

0:00

04:52

02:06

04:46

03:16

Hello. Welcome to this lesson. In this lesson, we'll use that comparison test to show whether the whole of the integral converges or diverges. So what, we'll compare it against this. So we have one over skirt of X four minus X, and this is always greater than one over X okay, or better than or equal to. But we know that the script of, uh, the integral from one to infinity of one of our x dx mhm that is equal to land X from one to infinity. That is a call to infinity minus one diver. Jeez. So if if this diverges, then the whole of this X plus one cool. So the idea here is that if gee of eggs 15 years Jean of X is less than f of X and then of X diabetes, Ben F of X will diverge, given the same the same bounce. Okay, sometimes your time. This is the end of the lesson.

View More Answers From This Book

Find Another Textbook

04:33

FInd sequence of elementary matrices that can be used to write the matrix in…

02:53

112Brianna's position on a Ferris wheel can be the function modelle…

07:00

The base and top of a rectangular covered box are three times as long as the…

blood pressure measurement consists of two numbers: the systolic pressure , …

02:13

Consider the relationship between the number of bids an item on eBay receive…

10:05

point) Let Pz be the vector space of polynomials of degree 2 or less Conside…

02:15

determining the best companies to work for; a number of variables are consid…

03:28

An entomologist has an insect colony for an experiment: The population of in…

01:58

PRovE Zdent(TY 2 2 I-si X Sin / ' Cot X = -Cosx Spck TAN + SIN Xe

01:11

Use the substitution u = 8x2 + x to evaluate the indefinite integral below. …