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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.

  • 22 Questions around this concept.

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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)

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

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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}}

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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

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Reference Books

Fundamental Formulae of Indefinite Integration (Trigonometric Functions)

Mathematics for Joint Entrance Examination JEE (Advanced) : Calculus

Page No. : 7.1

Line : 40

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