Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
1. (a) Compute dx sin³ (x) using the substitution t = tan(x/2). Later in this course: If R(u, v) is a rational function in u and v and we are interested in the case of an integral of the form li R(cos(x), sin(x))dx, then t = tan(x/2) is an effective (albeit not always an efficient) substitution. (b) Compute dx (sin(x) + cos(x))² ✓ using the substitution t = tan(x). Later in this course: If R(u, v) is a rational function in u and v as before or r(u) is a rational function in u and we are interested in the case of an integral of the form [ R(cos²(2), sin²(x))dr or [ r(tan(x))dæ then a more convenient substitution than the one in part (a) is t = tan(x).

1. (a) Compute dx sin³ (x) using the substitution t = tan(x/2). Later in this course: If R(u, v) is a rational function in u and v and we are interested in the case of an integral of the form li R(cos(x), sin(x))dx, then t = tan(x/2) is an effective (albeit not always an efficient) substitution. (b) Compute dx (sin(x) + cos(x))² ✓ using the substitution t = tan(x). Later in this course: If R(u, v) is a rational function in u and v as before or r(u) is a rational function in u and we are interested in the case of an integral of the form [ R(cos²(2), sin²(x))dr or [ r(tan(x))dæ then a more convenient substitution than the one in part (a) is t = tan(x).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
1. (a) Compute dx sin³ (x) using the substitution t = tan(x/2). Later in this course: If R(u, v) is a rational function in u and v and we are interested in the case of an integral of the form li R(cos(x), sin(x))dx, then t = tan(x/2) is an effective (albeit not always an efficient) substitution. (b) Compute dx (sin(x) + cos(x))² ✓ using the substitution t = tan(x). Later in this course: If R(u, v) is a rational function in u and v as before or r(u) is a rational function in u and we are interested in the case of an integral of the form [ R(cos²(2), sin²(x))dr or [ r(tan(x))dæ then a more convenient substitution than the one in part (a) is t = tan(x).
Transcribed Image Text:1. (a) Compute dx sin³ (x) using the substitution t = tan(x/2). Later in this course: If R(u, v) is a rational function in u and v and we are interested in the case of an integral of the form li R(cos(x), sin(x))dx, then t = tan(x/2) is an effective (albeit not always an efficient) substitution. (b) Compute dx (sin(x) + cos(x))² ✓ using the substitution t = tan(x). Later in this course: If R(u, v) is a rational function in u and v as before or r(u) is a rational function in u and we are interested in the case of an integral of the form [ R(cos²(2), sin²(x))dr or [ r(tan(x))dæ then a more convenient substitution than the one in part (a) is t = tan(x).
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS