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

Use the Table of Integrals on Reference Pages 6-10 to evaluate the integral. $ \displaystyle \int \frac{\cos^{-1} (x^{-2})}{x^3}\ 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 Foster Wisusik

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 6

Integration Using Tables and Computer Algebra Systems

Integration Techniques

Missouri State University

Campbell University

University of Michigan - Ann Arbor

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.

02:00

Use the Table of Integrals…

02:23

01:16

02:43

03:56

03:20

04:09

02:30

03:14

Use the Table of Integral…

02:41

03:28

03:07

02:47

Okay, This question wants us to integrate this function. So to do that, we want to transform this into the integral into one of our forms in the table. So to do this, let's make the substitution to make that transformation have. So we get you equal to X to the minus two. Because usually picking the argument of a coastline is a good start. So that makes d'you equal to negative, too. X to the minus three d x and we have X to the minus three d x. So we just gotta divide by negative too. So now we can transform are integral into negative 1/2 times the integral of co sign inverse of you, do you? And that's a much simply looking for him so we can look it up here, which gives us a formula for anti derivative. So let's just copy that down, keeping our negative 1/2 outside. So this is our anti derivative and now all we have to dio is substitute back in for you. So we get negative 1/2 times X to the negative to co sign in verse of X to the negative too minus square root of one minus X to the minus forth plus C and simplifying We get one over two X squared co sign in verse of one over X squared plus 1/2 square root one minus extra, the fourth plus C and that's your final answer.

View More Answers From This Book

Find Another Textbook

00:47

Question 2. (16 marks) Anouterplanar graph is simple graph that has planar d…

01:23

a)_ Find the matrix [T]B of the linear transformation T : V _ V relative to …

04:07

7 The plane w + y + 2 = 1 cuts the cylinder z2 + y? = 1 in an ellipse in R:_…

07:10

The velocity vector field for two dimensional flow of an ideal fluid around …

05:27

Below is the graph of f' (z); the graph of the derivative of f:Answ…

05:29

Evaluate the line integral [eadr for the following vector field F and curve …

08:20

-12.63 POINTSTANFIN12 7.1.022.An experiment consists 0f casting pair…

01:14

Question 5 of 10 2 PointsSAT scores are normally distributed, with a mea…

02:08

Follow the nine-step graphing strategy to sketch the graph of the rational f…

01:05

7/6 The arbor press works by & rack and pinion and is used to develop la…