UrbanPro
true

Take Class 12 Tuition from the Best Tutors

  • Affordable fees
  • 1-1 or Group class
  • Flexible Timings
  • Verified Tutors

Search in

Solution to a trigonometric problem using Weierstrass substitution

B.Sudhakar
02/01/2017 0 1

Let us solve one problem using Weierstrass substitution

∫ 1/(1 + cos x + sin x) dx     applying Weierstrass substitution

t= tan x/2 , sin x = 2 t/(1 + t²), cos x= 1 - t²)/ (1 + t²) , dx= 2 dt/ (1 + t²)

= ∫ 1/ 1 +( 1 - t²/1 + t²) + (2 t / 1 + t²) • 2/1 + t² dt 

= 2 ∫ 1/ 1 + 1 - t²/1 + t² + 2 t /1 + t² • 1/1 + t² dt 

= 2 ∫ 1/ [ (1 + t² + 1 - t² + 2 t) / (1 + t²) ] • (1/1 + t²) dt { take common denominator}

= 2 ∫ 1/ [ (2 + 2 t) / (1 + t²) ] • 1/(1 + t²) dt 

= 2 ∫ (1 + t²) / (2 + 2 t) • ( 1 + t² ) dt                { (1 + t²) cancels out }

= 2 ∫ 1 / (2 + 2 t) dt 

= 2 ∫ 1 / 2 ( 1 + t ) dt 

= 2/2 ∫ 1/ ( 1 + t ) dt 

= ∫ 1/ ( 1 + t ) dt 

= ln | 1 + t | dt + C                                              { substituting back t = tan x/2 }

= ln | 1 + tan x/2 | + C 

0 Dislike
Follow 0

Please Enter a comment

Submit

H

Harsha | 07/01/2017

Unknown to me ? Never heard of it. Quite useful

0 0

Other Lessons for You

4 Things Every Tech Startup Needs to Know About The Coaching Industry
Knowledge on any subject is widely available to those who wish to learn. However, just gathering knowledge from other people doesn’t guarantee results in business. Results come from applying what...

Internet of Things, Social Media Becoming Part of E-Discovery Landscape
The days when e-discovery consisted of handing over copies of e-mails to address Freedom of Information Act (FOIA) requests, compliance regulations or other legal obligations are over. Now, it's just as...

For IIT/NEET Aspirants Class 12 Chemistry - Reactivity Of Complexes With Hcl
More the electron density on the metal more will be the rate of oxidative addition. And hence increases the reactivity of complexes with HCL.

Sequencing types for class 12th biotechnology
Content of the notes: It is accompanied with following topics: DNA sequencing /Genome sequencing Methods of sequencing (DNA/GENOME) Expressed sequence tags(EST) Sequence tag-sites(STS) Some techniques...

Rajat Sharma

0 0
0

X

Looking for Class 12 Tuition Classes?

The best tutors for Class 12 Tuition Classes are on UrbanPro

  • Select the best Tutor
  • Book & Attend a Free Demo
  • Pay and start Learning

Take Class 12 Tuition with the Best Tutors

The best Tutors for Class 12 Tuition Classes are on UrbanPro

This website uses cookies

We use cookies to improve user experience. Choose what cookies you allow us to use. You can read more about our Cookie Policy in our Privacy Policy

Accept All
Decline All

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 55 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 7.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more