Homework Help is Here – Start Your Trial Now!
Math
Calculus
4. 16x – 2x2 – 23 dx -

4. 16x – 2x2 – 23 dx -

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.4: Multiple-angle Formulas
Problem 72E
See similar textbooks
icon
Related questions
Question
Trigonometric Substitution There are certain integrals that contain no trigonometry that can be solved with the aid of trigonometry. Consider integrands involving va? -x, a? +x, or vx - a (where a is constant). These can be evaluated by making the following substitutions. Va? + x x= asin 6 x= atan 0 X= asec 0 dx = acos ede dx = a sec*o de dx = asec Otan ede For each integral, figure out which trigonometric substitution should be used. The goal is to rewrite the integrand so that there is no radical. After integrating, draw and label a right triangle (as shown below). This will allow you to rewrite your integrated expression back in terms of x. For this last part of the problem, you may need one or more trigonometric identities. For example, the triangle that corresponds with exercise 1 looks like this. If we let x = 2sin 0, it follows that sin 6 = x/2. By expressing the side length opposite the given angle as x and the hypotenuse as 2, the side length adjacent the given angle works out conveniently to 4 -x, which is the integrand. !3!
Transcribed Image Text:Trigonometric Substitution There are certain integrals that contain no trigonometry that can be solved with the aid of trigonometry. Consider integrands involving va? -x, a? +x, or vx - a (where a is constant). These can be evaluated by making the following substitutions. Va? + x x= asin 6 x= atan 0 X= asec 0 dx = acos ede dx = a sec*o de dx = asec Otan ede For each integral, figure out which trigonometric substitution should be used. The goal is to rewrite the integrand so that there is no radical. After integrating, draw and label a right triangle (as shown below). This will allow you to rewrite your integrated expression back in terms of x. For this last part of the problem, you may need one or more trigonometric identities. For example, the triangle that corresponds with exercise 1 looks like this. If we let x = 2sin 0, it follows that sin 6 = x/2. By expressing the side length opposite the given angle as x and the hypotenuse as 2, the side length adjacent the given angle works out conveniently to 4 -x, which is the integrand. !3!
4. V16x- 2x2-23 dx
Transcribed Image Text:4. V16x- 2x2-23 dx
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Indefinite Integral
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS