Careers360 Logo
Engineering and Architecture
Search Colleges, Exams, Schools & more
JCECE Eligibility Criteria 2024: Age Limit, Qualification, Domicile
  1. Home
  2. JEE Main
  3. Study Material
  4. Integration of Trigonometric Functions - Practice Questions & MCQ

Integration of Trigonometric Functions - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Fundamental Formulae of Indefinite Integration (Trigonometric Functions) is considered one of the most asked concept.

  • 20 Questions around this concept.

Solve by difficulty

QuestionMEDIUM

The integral \small \int \sqrt{1 + 2cot x ( cosec x + cot x) dx} \small \left ( 0< x< \frac{\pi }{2} \right ) is equal to (where C is a constant of integration)

View Solution

Evaluate the integral of \int\left ( 4sin\ x+3cos\ x-2sec^{2}x \right )dx.

View Solution

Concepts Covered - 1

Fundamental Formulae of Indefinite Integration (Trigonometric Functions)

Trigonometric Functions

\\\mathrm{1.\;\;\frac{d}{d x}(-\cos x)=\sin x \Rightarrow \int \sin x\; d x=-\cos x+C}\\\\\mathrm{2.\;\;\frac{d}{d x}(sin x)=\cos x \Rightarrow \int \cos x\; d x=\sin x+C}\\\\\mathrm{3.\;\;\frac{d}{d x}(\tan x)=\sec ^{2} x \Rightarrow \int \sec ^{2} x \;d x=\tan x+C}\\\\\mathrm{4.\;\;\frac{d}{d x}(-\cot x)=\csc ^{2} x \Rightarrow \int \csc ^{2} x\; d x=-\cot x+C}\\\\\mathrm{5.\;\;\frac{d}{d x}(\sec x)=\sec x \tan x\;\Rightarrow \int \sec x \tan x\; d x=\sec x+C}\\\\\mathrm{6.\;\;{\frac{d}{d x}(-\csc x)=\csc x \cot x} \\ {\;\Rightarrow \int \csc x \cot x \;d x=-\csc x+C}}

Integrals of tan x, cot x, sec x, cosec x

\\\\\mathrm{7.\;\;{\frac{d}{d x}(\log |\sin x|)=\cot x} \\ {\;\Rightarrow \int \cot x \;d x=\log |\sin x|+C}}\\\\\mathrm{8.\;\;{\frac{d}{d x}(-\log |\cos x|)=\tan x} \\ {\;\Rightarrow \int \tan x \;d x=-\log |\cos x|+C}}\\\\\mathrm{9.\;\;{\frac{d}{d x}(\log |\sec x+\tan x|)=\sec x} \\ {\;\Rightarrow \int \sec x \;d x=\log |\sec x+\tan x|+C}}\\\\\mathrm{10.\;\;{\frac{d}{d x}(\log |\csc x-\cot x|)=\csc x} \\ {\;\Rightarrow \int \csc x \;d x=\log |\csc x-\cot x|+C}}

Study it with Videos

Fundamental Formulae of Indefinite Integration (Trigonometric Functions)

Study other Related Concepts

Integration of Trigonometric Functions Current Topic

Integration as an Inverse Process of Differentiation
Integration of Trigonometric Functions
Integration by Substitution
Fundamental Formulae of Indefinite Integration (Inverse Trigonometric Functions)
Integrals of Particular Function
Trigonometric Integrals
Integration By Parts Formula
Integration Using Partial Fraction
Integration of Irrational Algebraic Function
Reduction Formula

"Stay in the loop. Receive exam news, study resources, and expert advice!"

Books

Reference Books

Fundamental Formulae of Indefinite Integration (Trigonometric Functions)

Mathematics for Joint Entrance Examination JEE (Advanced) : Calculus

Page No. : 7.1

Line : 40

Clear your Basics with NCERT

E-books & Sample Papers

JEE Seat Matrix

8019+ Downloads

Get Answer to all your questions

JEE Main Articles

JEE Main Registration 2025- Application Date, Fees, Documents Required
May 15, 2024
JEE Main Eligibility Criteria 2025- Age Limit, Marks Required in Class 12
May 15, 2024
Two Months Preparation Plan for JEE Main and JEE Advanced 2024
May 15, 2024
Top Engineering Colleges without 75% Criteria in India 2024
May 13, 2024
JEE Main 2025 - Exam Date, Eligibility, Registration, Preparation Tips, Previous Year Papers
May 13, 2024
JCECE Application Form 2024, Registration (Started) - Apply Online here
May 13, 2024
JEE Main Marks vs Percentile vs Rank 2024 - How to Calculate Percentile using Marks
May 13, 2024
JEE Main Cutoff 2024 (Out) - Qualifying Marks for NITs, IIITs, GFTIs
May 13, 2024

B.Tech/B.Arch Admissions OPEN

Amity University, Noida B.Tech Admissions 2024
Amity University, Noida B.Tech Admissions 2024
Apply

Asia's Only University with the Highest US & UK Accreditation

UPES B.Tech Admissions 2024
UPES B.Tech Admissions 2024
Apply

Ranked #52 among universities in India by NIRF | Highest CTC 50 LPA | 100% Placements | Last Date to Apply: 31st May

Jain University B.Tech 2024
Jain University B.Tech 2024
Apply

100% Placement Record | Highest CTC 42 LPA | NAAC A++ Accredited | Ranked #68 in India by NIRF Ranking 2023 | Last Date to Apply: 17th May

ICFAI University Hyderabad B.Tech Admissions 2024
ICFAI University Hyderabad B.Tech Admissions 2024
Apply

Merit Scholarships | NAAC A+ Accredited | Top Recruiters : E&Y, CYENT, Nvidia, CISCO, Genpact, Amazon & many more

Pimpri Chinchwad University B.Tech Admissions
Pimpri Chinchwad University B.Tech Admissions
Apply

1000+ Recruiters | 450+ Patents | 50000+ Alumni network

Hindusthan College of Engineering & Tech Admissions 2024
Hindusthan College of Engineering & Tech Admissions 2024
Apply

Ranked #31 by Education World

View All Application Forms
News and Notifications
May 01, 2024 - 09:04 AM IST :
April 24, 2024 - 11:38 PM IST :
April 22, 2024 - 11:55 AM IST :
JEE Main 2024: NTA debars 39 candidates for 3 years on account of using unfair means
May 02, 2024 - 10:31 AM IST
JEE Main 2024 session 2 paper 2 answer key objection window closes today; fees
May 01, 2024 - 08:44 AM IST
JEE Main 2024 Topper: Farmer’s son Gajare Nilkrishna says ‘keep questioning until you understand’
April 25, 2024 - 05:07 PM IST
NIT Puducherry Cut-off 2024: Computer Science and Engineering had highest closing rank last year
April 25, 2024 - 11:16 AM IST
JEE Mains: Farmer's son from remote Maharashtra village aces exam
April 25, 2024 - 09:44 AM IST
What after JEE Main results 2024? All you need to know about JEE Adv, CSAB, JoSAA counselling
April 25, 2024 - 09:11 AM IST
JEE Main Toppers 2024: 56 candidates get 100 NTA score; mostly from Telangana, Maharashtra
April 24, 2024 - 11:36 PM IST

Download Careers360 App's

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

  • student
    300M+

    Students

  • colleges
    36,000+

    Colleges

  • exams
    550+

    Exams

  • ebook
    1500+

    E-Books

  • certification
    16000+

    Certifications

student
Mobile Screen

We Appeared in

Joint Entrance Examination (Main)      
JEE Main College Predictor
Back to top