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

Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take $ C = 0 $).

$ \displaystyle \int \tan^2 \theta \sec^2 \theta \, d\theta $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Amrita Bhasin

Numerade Educator

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

00:56

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 5

The Substitution Rule

Integration

Missouri State University

Baylor University

Boston College

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

07:15

Evaluate the indefinite in…

01:46

05:18

04:43

01:16

01:11

01:59

01:26

05:26

03:29

06:20

04:23

04:11

01:34

evaluate the integral, and…

given the fact that are you is tan of data. This means that d u over D thing that's the same thing is do you over dx except for instead of X. They've got data on this context is seeking square data. Therefore, we know that d you just written in terms of do you a secret scrub data d theta. Now we have the integral of you scored. Do you? We can integrate this to BU cubed over three years in the power rule, increased export by one divide by the new exponents And now back substituting end we end up with are integral now chek of our answers Reasonable weaken graph and you can see over here this is a reasonable answer.

View More Answers From This Book

Find Another Textbook