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Problem

Evaluate the integral. $ \displaystyle \int \l…

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Problem 9 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int \cos^{-1} x dx $


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Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

Related Topics

Integration Techniques

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01:53

Integration Techniques - Intro

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.

Video Thumbnail

27:53

Basic Techniques

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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Watch More Solved Questions in Chapter 7

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Problem 7
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Problem 9
Problem 10
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Problem 12
Problem 13
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Problem 15
Problem 16
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Problem 18
Problem 19
Problem 20
Problem 21
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Problem 23
Problem 24
Problem 25
Problem 26
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Problem 34
Problem 35
Problem 36
Problem 37
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Problem 39
Problem 40
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Problem 42
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Problem 45
Problem 46
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Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
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Problem 62
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Problem 66
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Problem 68
Problem 69
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Problem 73
Problem 74

Video Transcript

The problem is evaluated the integral integral cosine numerous x dx. For this problem we will use the method of integration by parts, so the formula is integral: u v, primedxis equal to? U times, v, minus integral? U, prime with the x now for this problem. We can let? U is equal to a sine us x and the last from is equal to 1. Then we have. U, prime, is equal to negative 1 over root of 1 minus x square and v is equal to x. Now use this formula. We have this integral is equal to cosin, inverse x times x, minus the integral negative 1 over root of 1 minus x square times x dx. This is equal to x, cosine, universe, x, plus integral x, over root of 1 minus x squared dx. For this part, we can use the method of u substitution and let? U is equal to 1 minus x square and d? U is equal to negative 2 x dx, so this integral is equal to negative, integral 1 half times u to negative 1 half du. This is equal to negative: u to 1 half. This is negative root of 1 minus x square. Now we know the integral of cosine inverse x dx. This is equal to x times, cosine numerus x and then, as the integral is 1, that minus the root of 1 minus x square, and it don't forget, as of constant number.

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Related Topics

Integration Techniques

Top Calculus 2 / BC Educators
Kayleah Tsai

Harvey Mudd College

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Joseph Lentino

Boston College

Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:53

Integration Techniques - Intro

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.

Video Thumbnail

27:53

Basic Techniques

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

Join Course
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Evaluate the integral. $\int \cos ^{-1} x d x$

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Evaluate the integral. $$ \int \cos ^{-1}(2 x) d x $$

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Evaluate the integral. $$\int \frac{\cos (1 / x)}{x^{2}} d x$$

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Evaluate the integral. $ \displaystyle \int \frac{\cos x}{1 - \sin x}\ dx $

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Evaluate the following integrals. $$\int \cos ^{-1} x d x$$

01:19

Evaluate the indicated integral. $$\int \frac{\cos (1 / x)}{x^{2}} d x$$

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