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

The region under the curve $ y = \sin^2 x $ from …

02:53

Question

Answered step-by-step

Problem 32 Medium Difficulty

Use the Table of Integrals on Reference Pages 6-10 to evaluate the integral.

$ \displaystyle \int \frac{\sec^2 \theta \tan^2 \theta}{\sqrt{9 - \tan^2 \theta}}\ d \theta $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Foster Wisusik
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Foster Wisusik

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 6

Integration Using Tables and Computer Algebra Systems

Related Topics

Integration Techniques

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Grace He
Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

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

04:13

Use the Table of Integrals…

01:58

$5-32$ Use the Table of In…

01:28

Use the Table of Integrals…

05:30

Use the Table of Integrals…

03:19

Use the Table of Integrals…

01:13

Use the Table of Integrals…

02:59

Use the Table of Integral…

05:50

Use the Table of Integrals…

05:36

Use the Table of Integrals…

03:58

Use the Table of Integrals…

02:23

Use the Table of Integrals…

02:17

Use the Table of Integrals…

03:05

Use the Substitution Formu…

02:41

Use the Table of Integrals…

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

Video Transcript

Okay, so this question wants us to find the integral of this function. So to do that, let's convert it to one of the forms that we can look up in our table easily. So a rule of thumb is that we always like to have a use squared in that denominator in the radical. So let's pick you to be equal to tangent data because then we get a nine minus you square down there. So taking d'you we've see that that's C can't squared data d theta, which is convenient because we already have that. So that's all we have to D'oh! So now we can just rewrite this as the integral of well, tangents squared is you squared, Do you? Over square root of nine minus you squared. So now from here, this looks very similar to one of our forms in the table which has this formula. So in this case, A is equal to three because we have a nine, which is three squared. So now our anti derivative is negative. You over too square root nine minus you squared, plus a squared over two, which is nine divided by two times sine inverse of you divided by a, which is plus C So now all we got to Dio is plug back in tangent data for you and we're done. So we get negative. 10th 8 over to square view nine minus 10 square data plus nine halves times the inverse sine of 10th ADA divided by three plus our integration constant. 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
192
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
83
Hosted by: Alonso M
See More

Related Topics

Integration Techniques

Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

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

04:13

Use the Table of Integrals on the Reference Pages to evaluate the integral. $$ …

01:58

$5-32$ Use the Table of Integrals on Reference Pages $6-10$ to evaluate the int…

01:28

Use the Table of Integrals on Reference Pages $6-10$ to evaluate the integral. …

05:30

Use the Table of Integrals on Reference Pages 6-10 to evaluate the integral. …

03:19

Use the Table of Integrals on Reference Pages 6-10 to evaluate the integral. …

01:13

Use the Table of Integrals on Reference Pages $6-10$ to evaluate the integral. …

02:59

Use the Table of Integrals on Reference Pages $6-10$ to evaluate the integral.…

05:50

Use the Table of Integrals on the Reference Pages to evaluate the integral. $$ …

05:36

Use the Table of Integrals on the Reference Pages to evaluate the integral. $$ …

03:58

Use the Table of Integrals on the Reference Pages to evaluate the integral. $$ …

02:23

Use the Table of Integrals on Reference Pages 6-10 to evaluate the integral. …

02:17

Use the Table of Integrals on Reference Pages 6-10 to evaluate the integral. …

03:05

Use the Substitution Formula in Theorem 7 to evaluate the integrals. $$\int_{0}…

02:41

Use the Table of Integrals on Reference Pages 6-10 to evaluate the integral. …
Additional Mathematics Questions

01:44

a sample of 500 adults found tgst 95 do not like cold weather. hiwever 114 o…

03:07

You can afford a $200 per month car payment. You've found a 3
year l…

02:01

Suppose Eddie takes out a loan for $4500 with an annual interest
rate of …

03:13

Given the function 𝑓(𝑥) = ln(𝑥 + 1) , 𝑥 > 0
a) Find the first derivat…

03:18

Suppose you can afford to pay $ 425 a month for 10 years towards
a new ca…

02:25

The journal entry to record the use of utilities in a factory
includes wh…

01:59

The coordinates of one endpoint of a line segment is (-4, 3), and the midpoi…

23:59

a) Consider the complex number z = 3 + 3i.
Find its conjugate, bar(z), a…

04:18

For each of the trigonometric functions below, give two other
angles θ th…

02:12

A bond that contains an option for the holder to convert the
bond to shar…

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