Evaluate the integral. [TI/3 2 sin(0) + 2 sin(0) tan2(0) sec2(0) de Step 1 2 sin(0) + 2 sin(0) tan²(8) we will first re-write the fraction. To find an antiderivative of f(0) sec2(0) Factoring out 2 sin(0) in the numerator gives us 2 sin(8) (1 + tan(0) 2 2 sin(0) + 2 sin(e) tan²(0) sec?(8) 1+ (tan (0))² f(0) sec?(0) Step 2 We know by a trigonometric identity that 1 + tan?(0) = sec(0)² sec2 (0) Step 3 *T/3 /3 2 sin(0) + 2 sin(8) tan2(0) sec?(0) 2 sin (0) As a result, we have de = 2 sin (0) de. Step 4 An antiderivative of sin(0) is Cukui

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
icon
Related questions
Question
Evaluate the integral.
[T/3 2 sin(@) + 2 sin(0) tan2(0)
sec?(0)
de
Step 1
2 sin(0) + 2 sin(0) tan2(0)
sec2(0)
To find an antiderivative of f(0)
we will first re-write the fraction.
Factoring out 2 sin(0) in the numerator gives us
2 sin(0) + 2 sin(0) tan2(0)
sec2(0)
2 sin(0) (1+ tan(0)2
f(0)
1+ (tan (0))² |
sec2(0)
Step 2
We know by a trigonometric identity that 1 + tan?(0) = sec (0)-
sec2 (0)
Step 3
* 1/3 2 sin(0) + 2 sin(0) tan2(0)
T/3
|2 sin (0)
As a result, we have
2 sin (0) de.
sec?(e)
Step 4
An antiderivative of sin(0) is
Submit
Skip (you cannot come back)
Transcribed Image Text:Evaluate the integral. [T/3 2 sin(@) + 2 sin(0) tan2(0) sec?(0) de Step 1 2 sin(0) + 2 sin(0) tan2(0) sec2(0) To find an antiderivative of f(0) we will first re-write the fraction. Factoring out 2 sin(0) in the numerator gives us 2 sin(0) + 2 sin(0) tan2(0) sec2(0) 2 sin(0) (1+ tan(0)2 f(0) 1+ (tan (0))² | sec2(0) Step 2 We know by a trigonometric identity that 1 + tan?(0) = sec (0)- sec2 (0) Step 3 * 1/3 2 sin(0) + 2 sin(0) tan2(0) T/3 |2 sin (0) As a result, we have 2 sin (0) de. sec?(e) Step 4 An antiderivative of sin(0) is Submit Skip (you cannot come back)
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning