Download the App!

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

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Use a graph of the integrand to guess the value o…

03:09

Question

Answered step-by-step

Problem 58 Hard Difficulty

Find the area of the region bounded by the given curves.

$ y = \tan x $ , $ y = \tan^2 x $ , $ 0 \le x \le \frac{\pi}{4} $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

JH
J Hardin
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by J Hardin

Numerade Educator

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

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 2

Trigonometric Integrals

Related Topics

Integration Techniques

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Anna Marie Vagnozzi

Campbell University

Kristen Karbon

University of Michigan - Ann Arbor

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
Recommended Videos

13:47

Find the area of the regio…

04:49

Find the area of the regio…

0:00

Find the area of the regio…

07:52

Find the area of the regio…

05:12

Find the area of the regio…

03:59

Find the area of the regio…

02:47

Sketch the region bounded …

0:00

Find the area of the regio…

01:05

Find the area of the regio…

Watch More Solved Questions in Chapter 7

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70

Video Transcript

here we'd like to find the area of the region bounded by the curves. Ten x tan squared X for X between zero power for So here's a rough sketch of the graphs and let me explain why So, First of all, we know that can and tan squared or both zero on X zero and they're both won when excess power for now in between for exes between zero pyro for we have numbers. So we have tan and tan square. So we have zero less than our people two ten eggs less than equal to one on the interval. It's your own empire before, and I know that when you take a number between zero and one and you raise it to a higher power, their number itself gets smaller. So since the blue graph is a higher power of the same number ten, it's going to be smaller than the red graph. And so to confirm this, let's go to actual graphing calculator. So just this before the reddest hand, the bluest hand square and from zero to about power, for we see that the red graph is above the blue ref, so that tells us well First of all, we'LL have a formula for the area. So let's write that out. This area is the integral A to be so here. Zero power before of the absolute value of ten eggs Linus Tan square. And by our previous observation, we noticed that tan squared was below or less than or equal to ten eggs. This tells us that tan eggs minus ten square Dex is positive. And we can use this because if so, if this is positive, that means that the absolute value is just itself. So we can write this as in a girl zero power before ten eggs minus ten squared. Now let's go ahead and rewrite this zero power for CNX minus seek and squared X minus one. So we did here was use a path Agron identity to rewrite Tan Square a Sikh and squared minus one. We can evaluate all of these anti derivatives. The derivative of the tangent is natural log of absolute value of C can't. Here we have a minus tan X, and that becomes so we have a double minus their sort of plus X and rn points zero power for So it's going and plug in those end points. So is playing Pi over four first natural log seeking of Piper for his route, too. Since it's positive we can drop the absolute value there and then tangent apart before is one plus x. So plus power for and then when we plug in zero, we have natural log and it's seeking of zero is one tangent of zero zero and then plus zero. And we know that natural log of one zero So we could actually ignore this whole second term. And we're left over with our final answer. Ellen Route too minus one plus pirate for So that's our area, and that's our final answer.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
151
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
68
Hosted by: Alonso M
See More

Related Topics

Integration Techniques

Top Calculus 2 / BC Educators
Anna Marie Vagnozzi

Campbell University

Kristen Karbon

University of Michigan - Ann Arbor

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
Recommended Videos

13:47

Find the area of the region bounded by the given curves. $$ y=\tan x, \quad y=\…

04:49

Find the area of the region bounded by the given curves. $ y = \tan x $ , $ …

0:00

Find the area of the region bounded by the graphs of the given equations. $$ y=…

07:52

Find the area of the region bounded by the graphs of $y=\tan x$ and $y=\sec x$ …

05:12

Find the area of the region bounded by the given curves. $$y=\sin ^{2} x, \q…

03:59

Find the area of the regions enclosed by the lines and curves. $x=\tan ^{2} y$ …

02:47

Sketch the region bounded by the curves and find its area. $$y=\tan x, \quad y=…

0:00

Find the area of the region bounded by the given curves. $ y = \sin^2 x $ , …

01:05

Find the area of the region bounded by the given curves. $ y = \sin^2 x $ , …
Additional Mathematics Questions

03:48

The marketing manager for a nationally franchised lawn service
company wo…

01:39

Use the Empirical Rule. The mean speed of a sample of vehicles
along a st…

02:18

Two students are using gradient descent to compute parameters
for linear …

07:00

The following is an ordered set of data: 1, 4, p, 7, q, 10
The mean and t…

02:38

6. If the random variable X is normally
distributed with a mean of 75 an…

02:16

A bin of 5 electrical components is known to contain 2 that are
defective…

02:30

The US Department of Health and Human Services wants to know
whether the …

03:02

You are using a digital scale to measure the mass of a sample.
However yo…

02:10

the mean income of a group of sample observations is $500; the standard devi…

03:08

Suppose that IQ scores have a bell-shaped distribution with a
mean of 103…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started