Open App

Class 12 Exam > Class 12 Notes > Find integral of root tan x . - Class - 12

Find integral of root tan x . - Class - 12 - Class 12 PDF Download

Can u solve integration of √tan x?
Ref: https://edurev.in/question/643092/Can-u-solve-integration-of-√tan-x-

∫√(tan x) dx

Let tan x = t²

⇒ sec² x dx = 2t dt

⇒ dx = [2t / (1 + t⁴)]dt

⇒ Integral ∫ 2t² / (1 + t⁴) dt

⇒ ∫[(t² + 1) + (t² - 1)] / (1 + t⁴) dt

⇒ ∫(t² + 1) / (1 + t⁴) dt + ∫(t² - 1) / (1 + t⁴) dt

⇒ ∫(1 + 1/t² ) / (t² + 1/t² ) dt + ∫(1 - 1/t² ) / (t² + 1/t² ) dt

⇒ ∫(1 + 1/t² )dt / [(t - 1/t)² + 2] + ∫(1 - 1/t²)dt / [(t + 1/t)² -2]

Let t - 1/t = u for the first integral ⇒ (1 + 1/t² )dt = du

and t + 1/t = v for the 2nd integral ⇒ (1 - 1/t² )dt = dv

Integral
= ∫du/(u² + 2) + ∫dv/(v² - 2)

= (1/√2) tan^-1 (u/√2) + (1/2√2) log(v -√2)/(v + √2)l + c

= (1/√2) tan^-1 [(t² - 1)/t√2] + (1/2√2) log (t² + 1 - t√2) / t² + 1 + t√2) + c

= (1/√2) tan^-1 [(tanx - 1)/(√2tan x)] + (1/2√2) log [tanx + 1 - √(2tan x)] / [tan x + 1 + √(2tan x)] + c

The document Find integral of root tan x . - Class - 12 - Class 12 is a part of Class 12 category.

All you need of Class 12 at this link: Class 12

FAQs on Find integral of root tan x . - Class - 12 - Class 12

1. How do I find the integral of √(tan x)?

Ans. To find the integral of √(tan x), you can use the substitution method. Let u = √(tan x), then du = (1/2) sec^2 x dx. By substituting these values into the integral, you can simplify the expression and solve for the integral.

2. Is there a shortcut or formula to find the integral of √(tan x)?

Ans. Unfortunately, there is no specific shortcut or formula to directly find the integral of √(tan x). However, you can use integration techniques such as substitution, trigonometric identities, or integration by parts to simplify the expression and solve for the integral.

3. Can I use a calculator to find the integral of √(tan x)?

Ans. While calculators can be helpful for evaluating definite integrals, they may not be able to find the antiderivative or indefinite integral of √(tan x) directly. You would still need to use integration techniques to solve for the integral symbolically.

4. Are there any specific conditions or restrictions when finding the integral of √(tan x)?

Ans. When finding the integral of √(tan x), it is important to consider the domain of the function. Since tan x is undefined at odd multiples of π/2, you may need to restrict the domain of the integral accordingly. Additionally, be cautious of potential singularities or discontinuities that may affect the integral.

5. Can the integral of √(tan x) be expressed in terms of elementary functions?

Ans. The integral of √(tan x) does not have a simple expression in terms of elementary functions such as polynomials, exponentials, or trigonometric functions. It is considered to be a non-elementary integral. However, it can still be evaluated using integration techniques mentioned earlier.

Related Exams

Class 12

About this Document

	2.1K Views
	4.67/5 Rating
	Dec 19, 2024 Last updated

Document Description: Find integral of root tan x . - Class - 12 for Class 12 2024 is part of Class 12 preparation. The notes and questions for Find integral of root tan x . - Class - 12 have been prepared according to the Class 12 exam syllabus. Information about Find integral of root tan x . - Class - 12 covers topics like and Find integral of root tan x . - Class - 12 Example, for Class 12 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Find integral of root tan x . - Class - 12.

Introduction of Find integral of root tan x . - Class - 12 in English is available as part of our Class 12 preparation & Find integral of root tan x . - Class - 12 in Hindi for Class 12 courses. Download more important topics, notes, lectures and mock test series for Class 12 Exam by signing up for free. Class 12: Find integral of root tan x . - Class - 12 - Class 12

Description

Full syllabus notes, lecture & questions for Find integral of root tan x . - Class - 12 - Class 12 - Class 12 | Plus excerises question with solution to help you revise complete syllabus | Best notes, free PDF download

Information about Find integral of root tan x . - Class - 12

In this doc you can find the meaning of Find integral of root tan x . - Class - 12 defined & explained in the simplest way possible. Besides explaining types of Find integral of root tan x . - Class - 12 theory, EduRev gives you an ample number of questions to practice Find integral of root tan x . - Class - 12 tests, examples and also practice Class 12 tests.

Download as PDF

Explore Courses for Class 12 exam

Signup for Free!

Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.

Start learning for Free

10M+ students study on EduRev

Important questions

Previous Year Questions with Solutions

video lectures

Find integral of root tan x . - Class - 12 - Class 12

pdf

Summary

mock tests for examination

Sample Paper

Extra Questions

shortcuts and tricks

Find integral of root tan x . - Class - 12 - Class 12

Objective type Questions

past year papers

Semester Notes

Free

Exam

MCQs

practice quizzes

Viva Questions

ppt

study material

;

Additional Information about Find integral of root tan x . - Class - 12 for Class 12 Preparation

Find integral of root tan x . - Class - 12 Free PDF Download

The Find integral of root tan x . - Class - 12 is an invaluable resource that delves deep into the core of the Class 12 exam. These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective. With the help of these notes, you can grasp complex subjects quickly, revise important points easily, and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner, allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material, or toppers' notes, this PDF has got you covered. Download the Find integral of root tan x . - Class - 12 now and kickstart your journey towards success in the Class 12 exam.

Importance of Find integral of root tan x . - Class - 12

The importance of Find integral of root tan x . - Class - 12 cannot be overstated, especially for Class 12 aspirants. This document holds the key to success in the Class 12 exam. It offers a detailed understanding of the concept, providing invaluable insights into the topic. By knowing the concepts well in advance, students can plan their preparation effectively. Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.

Find integral of root tan x . - Class - 12 Notes

Find integral of root tan x . - Class - 12 Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to Find integral of root tan x . - Class - 12. It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation. Practice papers and question papers enable you to assess your progress effectively. Additionally, the paper analysis provides valuable tips for tackling the exam strategically. Access to Toppers' notes gives you an edge in understanding complex concepts. Whether you're a beginner or aiming for advanced proficiency, Find integral of root tan x . - Class - 12 Notes on EduRev are your ultimate resource for success.

Find integral of root tan x . - Class - 12 Class 12 Questions

The "Find integral of root tan x . - Class - 12 Class 12 Questions" guide is a valuable resource for all aspiring students preparing for the Class 12 exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation. The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level. Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.

Study Find integral of root tan x . - Class - 12 on the App

Students of Class 12 can study Find integral of root tan x . - Class - 12 alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the Find integral of root tan x . - Class - 12, students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc. The EduRev App will make your learning easier as you can access it from anywhere you want. The content of Find integral of root tan x . - Class - 12 is prepared as per the latest Class 12 syllabus.

Education Revolution