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
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
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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
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)
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