   Chapter 8.2, Problem 43E

Chapter
Section
Textbook Problem

# Evaluating a Definite Integral In Exercises 43-52, evaluate the definite integral. Use a graphing utility to verify your result. ∫ 0 1 / 2 arccos x   d x

To determine

To calculate: The value definite integral 012arccosxdx. And also verify the solution by using graphing utility.

Explanation

Given:the given definite integral is 012arccosxdx

Formula used:

By using Integral by part method

We have,,

udv=uvvdu

Calculation:

The integration we have,

012arccosxdx

In order to Find integration by part method ,

Let u=arccosx

On Differentiating the function u with respect to x

We get,

ddxu=ddx(cos1(x))dudy=11x2

And

dv=dx

Now, on integrating both sides.

We get,,

v=x

By using The above mentioned formula of integral by part,

i.e.

udv=uvvdu

Now, putting the values above

We get,

arccosxdx=xcos1xx1x2dx=xcos1x+121x2(2x)dx=xcos1x1x2+C

Now, by using antiderivative to find the value of integral

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 9 and 10, find the limit. limx3(2x23x+4)

Calculus: An Applied Approach (MindTap Course List)

#### Find the mean for the following set of scores: 2, 7, 9, 4, 5, 3, 0, 6

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

#### In Exercises 107-120, factor each expression completely. 109. 4a2 b2

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Find the limit. limx1+x29x2+2x3

Single Variable Calculus: Early Transcendentals 