Download the App!

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

Question

Answered step-by-step

Evaluate the integral.

$ \displaystyle \int \ln \sqrt{x} dx $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Wen Zheng

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

Integration Techniques

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

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.

03:15

Evaluate the integral.…

11:50

04:01

02:27

Evaluate the indefinite in…

The problem is, you violated the integral integral of n root of x d x for this problem. We cannot use the method of integration by powers, so the formula is integral of u v. Prim dx is equal to: u times, v minus integral of? U? Prime v d x for this problem we can not? U is equal to n rotonda prime is equal to 1. It then prime, is equal to here. We use the change rule. This is motive x, 12 x times. Integral of double x is 1 half times 1. Over root of x, so this is 1 over 2 x in v- is equal to x. Over have integral of x. Dx is equal to u times v, so this is x times n root of x minus integral of prim times. So this is 1 half the answer is x times: l n, o t of x, minus 1, half times x and plus the constant number c.

View More Answers From This Book

Find Another Textbook

factor and simplify: (x+5)^1/3 - (x+5)^4/3

03:36

The company is expected to pay its dividend today of $1.26. One year ago the…

06:46

The Harding Company manufactures skates. The company's income statement…

04:25

[The following information applies to the questions displayed below.] …

02:00

Quinn Corporation produces $2 million in profits with $28 million in sales. …

05:01

Shadee Corp. expects to sell 610 sun visors in May and 390 in June. Each vis…

00:53

suppose that you are rolling a six sided dice. let a = get a 3 what is p(ac)…

01:35

The length of a beam be 72 feet. If it is cut into 3 pieces in a ratio of 2:…

02:40

Suppose that the waiting time for a license plate renewal at a local office …